{"id":4931,"date":"2022-03-07T21:30:26","date_gmt":"2022-03-07T12:30:26","guid":{"rendered":"https:\/\/hatsudy.com\/jp\/?p=4931"},"modified":"2022-06-11T17:42:32","modified_gmt":"2022-06-11T08:42:32","slug":"combinations","status":"publish","type":"post","link":"https:\/\/hatsudy.com\/jp\/combinations.html","title":{"rendered":"\u7d44\u307f\u5408\u308f\u305b\uff08C\uff09\u306e\u516c\u5f0f\u3068\u9806\u5217\u30fb\u91cd\u8907\u7d44\u307f\u5408\u308f\u305b\u306e\u8a08\u7b97\u65b9\u6cd5"},"content":{"rendered":"\n<p>\u78ba\u7387\u306e\u8a08\u7b97\u3067\u91cd\u8981\u306a\u516c\u5f0f\u306b\u7d44\u307f\u5408\u308f\u305b\uff08C: Combinations\uff09\u304c\u3042\u308a\u307e\u3059\u3002\u516c\u5f0f\u3092\u5229\u7528\u3057\u306a\u3044\u5834\u5408\u3001\u7d44\u307f\u5408\u308f\u305b\u306e\u554f\u984c\u3092\u89e3\u304f\u306e\u306f\u96e3\u3057\u3044\u3067\u3059\u3002\u305f\u3060\u516c\u5f0f\u3092\u5229\u7528\u3059\u308c\u3070\u3001\u7c21\u5358\u306b\u7d44\u307f\u5408\u308f\u305b\u306e\u554f\u984c\u3092\u89e3\u304f\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<p>\u305f\u3060\u7d44\u307f\u5408\u308f\u305b\u3067\u306f\u5fdc\u7528\u554f\u984c\u304c\u983b\u7e41\u306b\u51fa\u3055\u308c\u307e\u3059\u3002\u305d\u3053\u3067\u6761\u4ef6\u304c\u52a0\u3048\u3089\u308c\u308b\u3068\u304d\u3001\u3069\u306e\u3088\u3046\u306b\u7d44\u307f\u5408\u308f\u305b\u306e\u516c\u5f0f\u3092\u5229\u7528\u3059\u308c\u3070\u3044\u3044\u306e\u304b\u7406\u89e3\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\u307e\u305f\u3001\u7d44\u307f\u5408\u308f\u305b\u3067\u306f\u300c\u540c\u3058\u3082\u306e\u3092\u542b\u3080\u9806\u5217\u300d\u306e\u8a08\u7b97\u3092\u3059\u308b\u3053\u3068\u304c\u3042\u308a\u307e\u3059\u3002\u307b\u304b\u306b\u306f\u3001\u540c\u3058\u5019\u88dc\u3092\u4f55\u5ea6\u9078\u3093\u3067\u3082\u554f\u984c\u306a\u3044\u7d44\u307f\u5408\u308f\u305b\u3067\u306f\u3001\u91cd\u8907\u7d44\u307f\u5408\u308f\u305b\u3068\u547c\u3070\u308c\u307e\u3059\u3002\u3053\u308c\u3089\u306f\u554f\u984c\u306e\u89e3\u304d\u65b9\u3092\u7406\u89e3\u3057\u3066\u3044\u306a\u3044\u3068\u7b54\u3048\u3092\u51fa\u3059\u306e\u304c\u96e3\u3057\u3044\u3067\u3059\u3002<\/p>\n<p>\u305d\u308c\u3067\u306f\u3001\u7d44\u307f\u5408\u308f\u305b\u306e\u516c\u5f0f\u3092\u5229\u7528\u3057\u3066\u3069\u306e\u3088\u3046\u306b\u554f\u984c\u3092\u89e3\u3051\u3070\u3044\u3044\u306e\u3067\u3057\u3087\u3046\u304b\u3002\u516c\u5f0f\u306e\u5229\u7528\u65b9\u6cd5\u3084\u540c\u3058\u3082\u306e\u3092\u542b\u3080\u9806\u5217\u3001\u91cd\u8907\u7d44\u307f\u5408\u308f\u305b\u306e\u8a08\u7b97\u65b9\u6cd5\u3092\u89e3\u8aac\u3057\u3066\u3044\u304d\u307e\u3059\u3002<\/p>\n<h2>\u9806\u756a\u3092\u8003\u616e\u3057\u306a\u3044\u5834\u5408\u304c\u7d44\u307f\u5408\u308f\u305b<\/h2>\n<p>\u9806\u5217\u3068\u7d44\u307f\u5408\u308f\u305b\u306f\u8a08\u7b97\u65b9\u6cd5\u304c\u7570\u306a\u308a\u307e\u3059\u3002\u9806\u5217\u3067\u306f\u9806\u756a\u304c\u91cd\u8981\u306b\u306a\u308a\u307e\u3059\u3002\u9806\u756a\u3092\u8003\u616e\u3059\u308b\u305f\u3081\u3001\u9806\u5217\u306e\u516c\u5f0f\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u3067\u4f55\u901a\u308a\u306e\u9806\u756a\u304c\u3042\u308b\u306e\u304b\u8a08\u7b97\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<p>\u4e00\u65b9\u3067<span style=\"color: #ff0000;\">\u7d44\u307f\u5408\u308f\u305b\u3067\u306f\u3001\u9806\u756a\u3092\u8003\u616e\u3057\u307e\u305b\u3093\u3002<\/span>\u4e26\u3079\u308b\u9806\u756a\u3092\u7121\u8996\u3057\u3066\u9078\u3076\u3068\u304d\u3001\u4f55\u901a\u308a\u306e\u65b9\u6cd5\u304c\u3042\u308b\u306e\u304b\u6570\u3048\u308b\u306e\u304c\u7d44\u307f\u5408\u308f\u305b\u3067\u3059\u3002\u4f8b\u3048\u3070\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p><strong>\u30fb\u30ab\u30fc\u30c9\u3092\u9078\u3076<\/strong><\/p>\n<ul>\n<li>\u9806\u5217\uff1a7\u679a\u306e\u30ab\u30fc\u30c9\u304b\u30893\u679a\u3092\u9078\u3073\u30013\u30b1\u30bf\u306e\u6570\u5b57\u3092\u4f5c\u308b\uff08\u5de6\u304b\u3089\u9806\u306b\u4e26\u3079\u308b\uff09<\/li>\n<li>\u7d44\u307f\u5408\u308f\u305b\uff1a7\u679a\u306e\u30ab\u30fc\u30c9\u304b\u30893\u679a\u3092\u9078\u3076<\/li>\n<\/ul>\n<p><strong>\u30fb\u4ee3\u8868\u8005\u306e\u6c7a\u5b9a<\/strong><\/p>\n<ul>\n<li>10\u4eba\u306e\u4e2d\u304b\u3089\u3001\u30ea\u30fc\u30c0\u30fc\u3068\u526f\u30ea\u30fc\u30c0\u30fc\u3092\u6c7a\u3081\u308b<\/li>\n<li>10\u4eba\u306e\u4e2d\u304b\u3089\u30012\u4eba\u306e\u30ea\u30fc\u30c0\u30fc\u3092\u6c7a\u3081\u308b<\/li>\n<\/ul>\n<p>\u30ab\u30fc\u30c9\u3092\u5de6\u304b\u3089\u9806\u306b\u4e26\u3079\u308b\u3068\u304d\u3001\u9806\u5217\u3092\u5229\u7528\u3057\u307e\u3059\u3002\u4e00\u65b9\u3067\u30ab\u30fc\u30c9\u3092\u9078\u3076\u3082\u306e\u306e\u3001\u9806\u756a\u3092\u8003\u616e\u3057\u306a\u3044\u5834\u5408\u306f\u7d44\u307f\u5408\u308f\u305b\u3092\u5229\u7528\u3057\u307e\u3059\u3002<\/p>\n<p>\u307e\u305f\u4ee3\u8868\u8005\u3092\u6c7a\u5b9a\u3059\u308b\u3068\u304d\u3001\u30ea\u30fc\u30c0\u30fc\u3068\u526f\u30ea\u30fc\u30c0\u30fc\u306f\u660e\u78ba\u306b\u533a\u5225\u3067\u304d\u307e\u3059\u3002\u307e\u305f\u30ea\u30fc\u30c0\u30fc\u3068\u526f\u30ea\u30fc\u30c0\u30fc\u3092\u9078\u3076\u3068\u3044\u3046\u306e\u306f\u3001\u300c\u30ea\u30fc\u30c0\u30fc\u3068\u526f\u30ea\u30fc\u30c0\u30fc\u306e\u9806\u306b\u4e26\u3079\u308b\u300d\u3053\u3068\u3068\u610f\u5473\u304c\u540c\u3058\u3067\u3059\u3002\u305d\u306e\u305f\u3081\u9806\u5217\u3092\u5229\u7528\u3057\u307e\u3059\u3002\u305f\u30602\u4eba\u306e\u30ea\u30fc\u30c0\u30fc\u306b\u3064\u3044\u3066\u306f\u3001\u4e21\u8005\u3092\u533a\u5225\u3067\u304d\u307e\u305b\u3093\u3002\u305d\u306e\u305f\u3081\u7d44\u307f\u5408\u308f\u305b\u3092\u5229\u7528\u3057\u307e\u3059\u3002<\/p>\n<p>\u3053\u306e\u3088\u3046\u306b\u3001\u9806\u756a\u3092\u8003\u616e\u3059\u308b\u306e\u304b\u3057\u306a\u3044\u306e\u304b\u306b\u3088\u3063\u3066\u9806\u5217\u3068\u7d44\u307f\u5408\u308f\u305b\u3092\u4f7f\u3044\u5206\u3051\u308b\u3088\u3046\u306b\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<h3>\u7d44\u307f\u5408\u308f\u305b\u306e\u516c\u5f0f\u3068\u8a08\u7b97\u65b9\u6cd5<\/h3>\n<p>\u305d\u308c\u3067\u306f\u3001\u7d44\u307f\u5408\u308f\u305b\u3067\u306f\u3069\u306e\u3088\u3046\u306b\u8a08\u7b97\u3059\u308c\u3070\u3044\u3044\u306e\u3067\u3057\u3087\u3046\u304b\u3002\u4f8b\u3048\u30706\u679a\u306e\u30ab\u30fc\u30c9\u304b\u30893\u679a\u3092\u9078\u3073\u3001\u5de6\u304b\u3089\u9806\u306b\u4e26\u3079\u308b\u5834\u5408\u3001<sub>6<\/sub>P<sub>3<\/sub>\u3068\u8868\u3057\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(_6P_3=6\u00d75\u00d74=120\\)<\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/03\/tru4.jpg\" alt=\"\" width=\"494\" height=\"333\" class=\"aligncenter size-full wp-image-4912\" \/><\/p>\n<p>\u4e00\u65b9\u3067\u5de6\u304b\u3089\u9806\u306b\u4e26\u3079\u305a\u30016\u679a\u306e\u30ab\u30fc\u30c9\u304b\u30893\u679a\u3092\u9078\u3076\u3068\u304d\u3001\u4f55\u901a\u308a\u306e\u65b9\u6cd5\u304c\u3042\u308b\u3067\u3057\u3087\u3046\u304b\u3002<span style=\"color: #0000ff;\">\u7d44\u307f\u5408\u308f\u305b\u3092\u5229\u7528\u3059\u308b\u5834\u5408\u3001P\u3092C\u306b\u5909\u3048\u307e\u3057\u3087\u3046\u3002<\/span>\u305d\u306e\u305f\u30816\u679a\u306e\u30ab\u30fc\u30c9\u304b\u30893\u679a\u3092\u9078\u3076\u5834\u5408\u3001<sub>6<\/sub>C<sub>3<\/sub>\u3068\u8868\u3057\u307e\u3059\u3002<\/p>\n<p>n\u500b\u306e\u4e2d\u304b\u3089r\u500b\u3092\u53d6\u308b\u5834\u5408\u3001<sub>n<\/sub>C<sub>r<\/sub>\u3068\u8868\u3055\u308c\u307e\u3059\u3002\u7d44\u307f\u5408\u308f\u305b\u306e\u8a18\u53f7\u3092\u5229\u7528\u3059\u308b\u3068\u304d\u3001P\u3092C\u306b\u5909\u3048\u308b\u3060\u3051\u3067\u3059\u3002<\/p>\n<p><strong>\u30fb\u7d44\u307f\u5408\u308f\u305b\u306e\u516c\u5f0f\u3092\u5229\u7528\u3059\u308b<\/strong><\/p>\n<p>\u6b21\u306b\u7d44\u307f\u5408\u308f\u305b\u306e\u516c\u5f0f\u3092\u5229\u7528\u3057\u3066\u8a08\u7b97\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3057\u3087\u3046\u3002<sub>6<\/sub>C<sub>3<\/sub>\u306f\u3069\u306e\u3088\u3046\u306b\u8a08\u7b97\u3059\u308c\u3070\u3044\u3044\u306e\u3067\u3057\u3087\u3046\u304b\u3002\u7d44\u307f\u5408\u308f\u305b\u306e\u516c\u5f0f\u3067\u306f\u5206\u6570\u3092\u5229\u7528\u3057\u307e\u3059\u3002n\u500b\u306e\u4e2d\u304b\u3089\u9078\u3076\u5834\u5408\u3001\u5206\u5b50\u306b\u306fn!\u3092\u7f6e\u304d\u307e\u3057\u3087\u3046\u3002\u307e\u305f\u5206\u6bcd\u3067\u306f\u3001\\(r!\\)\u3068\\((n-r)!\\)\u306e\u304b\u3051\u7b97\u3092\u3057\u307e\u3059\u3002<\/p>\n<p>\u305d\u306e\u305f\u3081\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u516c\u5f0f\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(_nC_r=\\displaystyle\\frac{n!}{r!(n-r)!}\\)<\/li>\n<\/ul>\n<p>\u516c\u5f0f\u3092\u898b\u308b\u3088\u308a\u3082\u3001\u5b9f\u969b\u306e\u8a08\u7b97\u3092\u78ba\u8a8d\u3059\u308b\u307b\u3046\u304c\u7406\u89e3\u3057\u3084\u3059\u3044\u3067\u3059\u3002\u4f8b\u3048\u3070\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(_5C_2=\\displaystyle\\frac{5!}{2!(5-2)!}=\\displaystyle\\frac{5!}{2!3!}\\)<\/li>\n<li>\\(_{10}C_7=\\displaystyle\\frac{10!}{7!(10-7)!}=\\displaystyle\\frac{10!}{7!3!}\\)<\/li>\n<li>\\(_8C_6=\\displaystyle\\frac{8!}{6!(8-6)!}=\\displaystyle\\frac{8!}{6!2!}\\)<\/li>\n<li>\\(_{100}C_{78}=\\displaystyle\\frac{100!}{78!(100-78)!}=\\displaystyle\\frac{100!}{78!22!}\\)<\/li>\n<\/ul>\n<p>\u3053\u306e\u3088\u3046\u306b\u3001C\u306e\u5de6\u3068\u53f3\u306b\u3042\u308b\u6570\u5b57\u3092\u78ba\u8a8d\u3057\u3066\u8a08\u7b97\u5f0f\u3092\u4f5c\u308a\u307e\u3059\u3002\u3053\u306e\u516c\u5f0f\u306f\u7d44\u307f\u5408\u308f\u305b\u306e\u8a08\u7b97\u3067\u983b\u7e41\u306b\u4f7f\u3046\u3053\u3068\u306b\u306a\u308b\u305f\u3081\u3001\u5fc5\u305a\u899a\u3048\u308b\u3088\u3046\u306b\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\u306a\u304a6\u679a\u306e\u30ab\u30fc\u30c9\u304b\u30893\u679a\u3092\u9078\u3076\u3068\u304d\u3001\u7d44\u307f\u5408\u308f\u305b\u306e\u516c\u5f0f\u3092\u5229\u7528\u3059\u308b\u3068\u3001\u524d\u306b\u793a\u3057\u305f\u3088\u3046\u306b<sub>6<\/sub>C<sub>3<\/sub>\u3068\u306a\u308a\u307e\u3059\u3002\u3053\u308c\u3092\u8a08\u7b97\u3059\u308b\u3068\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>\\(_6C_3=\\displaystyle\\frac{6!}{3!3!}=\\displaystyle\\frac{6\u00d75\u00d74\u00d73\u00d72}{3\u00d72\u00d73\u00d72}=20\\)<\/p>\n<p>\u3053\u3046\u3057\u3066\u300120\u901a\u308a\u304c\u7b54\u3048\u3068\u308f\u304b\u308a\u307e\u3059\u3002<\/p>\n<p>\u306a\u304a\u7d44\u307f\u5408\u308f\u305b\u3067\u306f\u3001<sub>n<\/sub>C<sub>0<\/sub>\uff1d<sub>n<\/sub>C<sub>n<\/sub>\uff1d1\u3068\u306a\u308a\u307e\u3059\u3002\u4f8b\u3048\u3070\u3001<sub>7<\/sub>C<sub>0<\/sub>\uff1d<sub>7<\/sub>C<sub>7<\/sub>\uff1d1\u3067\u3059\u30027\u500b\u306e\u4e2d\u304b\u3089\u4f55\u3082\u9078\u3070\u306a\u3044\u5834\u5408\u3001\u65b9\u6cd5\u306f1\u901a\u308a\u3067\u3059\u3002\u307e\u305f7\u500b\u306e\u4e2d\u304b\u3089\u3059\u3079\u3066\u9078\u3076\u5834\u5408\u3001\u65b9\u6cd5\u306f1\u901a\u308a\u3067\u3059\u3002\u305d\u306e\u305f\u3081\u3001<sub>n<\/sub>C<sub>0<\/sub>\uff1d<sub>n<\/sub>C<sub>n<\/sub>\uff1d1\u306b\u306a\u308b\u3068\u7406\u89e3\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\u307e\u305f\u516c\u5f0f\u3092\u7406\u89e3\u3059\u308c\u3070\u3001\u4f8b\u3048\u3070<sub>7<\/sub>C<sub>2<\/sub>\u3068<sub>7<\/sub>C<sub>5<\/sub>\u306f\u540c\u3058\u7b54\u3048\u306b\u306a\u308b\u3068\u308f\u304b\u308a\u307e\u3059\u3002\u4ee5\u4e0b\u306e\u8a08\u7b97\u5f0f\u306b\u306a\u308b\u304b\u3089\u3067\u3059\u3002<\/p>\n<ul>\n<li>\\(_7C_2=\\displaystyle\\frac{7!}{2!(7-2)!}=\\displaystyle\\frac{7!}{2!5!}\\)<\/li>\n<li>\\(_7C_5=\\displaystyle\\frac{7!}{5!(7-5)!}=\\displaystyle\\frac{7!}{5!2!}\\)<\/li>\n<\/ul>\n<p>\u3053\u306e\u3088\u3046\u306b\u3001\u540c\u3058\u8a08\u7b97\u5f0f\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<h3>\u5148\u306b\u7d04\u5206\u3092\u3057\u3066\u3001\u7d44\u307f\u5408\u308f\u305b\u306e\u8a08\u7b97\u3092\u65e9\u304f\u3059\u308b<\/h3>\n<p>\u5148\u307b\u3069\u3001\u7d44\u307f\u5408\u308f\u305b\u306e\u516c\u5f0f\u3092\u5229\u7528\u3059\u308b\u65b9\u6cd5\u3092\u89e3\u8aac\u3057\u307e\u3057\u305f\u3002\u305f\u3060\u8a08\u7b97\u3092\u3059\u308b\u3068\u304d\u3001\u3067\u304d\u308b\u3060\u3051\u8a08\u7b97\u304c\u7c21\u5358\u3067\u3042\u308b\u307b\u3069\u3044\u3044\u3067\u3059\u3002\u305d\u3053\u3067\u9806\u5217\u306e\u516c\u5f0f\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u306b\u3088\u3063\u3066\u3001\u7d44\u307f\u5408\u308f\u305b\u306e\u8a08\u7b97\u3092\u7d20\u65e9\u304f\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\u5177\u4f53\u7684\u306b\u306f\u3001\\(r!\\)\u3068\\((n-r)!\\)\u3092\u6bd4\u8f03\u3057\u3066\u3001\u6570\u5b57\u306e\u5927\u304d\u3044\u307b\u3046\u3068\u5206\u5b50\u3092\u4e8b\u524d\u306b\u7d04\u5206\u3057\u307e\u3059\u3002\u305d\u3046\u3059\u308b\u3068\u3001\u8a08\u7b97\u304c\u7c21\u5358\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>\u4f8b\u3048\u3070\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/03\/yykr12.jpg\" alt=\"\" width=\"600\" height=\"152\" class=\"aligncenter size-full wp-image-4933\" \/><\/p>\n<p>\u6163\u308c\u3066\u3044\u306a\u3044\u5834\u5408\u3001\u7d44\u307f\u5408\u308f\u305b\u306e\u516c\u5f0f\u3092\u5229\u7528\u3057\u3066\u8a08\u7b97\u3059\u308b\u3088\u3046\u306b\u3057\u307e\u3057\u3087\u3046\u3002\u4e00\u65b9\u3067\u7d44\u307f\u5408\u308f\u305b\u306e\u8a08\u7b97\u306b\u6163\u308c\u305f\u5834\u5408\u3001\u7d20\u65e9\u304f\u8a08\u7b97\u3059\u308b\u305f\u3081\u3001\u5148\u306b\u7d04\u5206\u3092\u3057\u3066\u5206\u6570\u3092\u7c21\u7565\u5316\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<h3>\u7d44\u307f\u5408\u308f\u305b\u3067\u91cd\u8981\u306a\u7d44\u307f\u5206\u3051\uff08\u30b0\u30eb\u30fc\u30d7\u306e\u533a\u5225\uff09\u306e\u554f\u984c<\/h3>\n<p>\u306a\u304a\u7d44\u307f\u5408\u308f\u305b\u306e\u554f\u984c\u3092\u89e3\u304f\u3068\u304d\u3001\u7d44\u307f\u5206\u3051\u306e\u554f\u984c\u304c\u983b\u7e41\u306b\u51fa\u3055\u308c\u307e\u3059\u3002\u3064\u307e\u308a<span style=\"color: #0000ff;\">\u30b0\u30eb\u30fc\u30d7\u3078\u5206\u3051\u308b\u3068\u304d\u3001\u533a\u5225\u3067\u304d\u308b\u304b\u3069\u3046\u304b\u78ba\u8a8d\u3057\u306a\u3051\u308c\u3070\u3044\u3051\u307e\u305b\u3093\u3002<\/span><\/p>\n<p>\u3069\u306e\u3088\u3046\u306b\u7b54\u3048\u3092\u51fa\u3059\u306e\u304b\u306b\u3064\u3044\u3066\u3001\u4ee5\u4e0b\u306e\u4f8b\u984c\u3092\u89e3\u3044\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/p>\n<ul>\n<li>12\u4eba\u3092\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u308f\u3051\u308b\u3068\u304d\u3001\u4f55\u901a\u308a\u306e\u65b9\u6cd5\u304c\u3042\u308a\u307e\u3059\u304b\uff1f<\/li>\n<\/ul>\n<ol style=\"list-style-type: lower-alpha;\">\n<li>5\u4eba\u30014\u4eba\u30013\u4eba\u306b\u5206\u3051\u308b<\/li>\n<li>4\u4eba\u305a\u3064A\u3001B\u3001C\u306e\u30b0\u30eb\u30fc\u30d7\u306b\u5206\u3051\u308b<\/li>\n<li>4\u4eba\u305a\u3064\u30013\u3064\u306e\u30b0\u30eb\u30fc\u30d7\u306b\u5206\u3051\u308b<\/li>\n<li>6\u4eba\u30013\u4eba\u30013\u4eba\u306e\u30b0\u30eb\u30fc\u30d7\u306b\u5206\u3051\u308b<\/li>\n<\/ol>\n<p><strong>(a) 5\u4eba\u30014\u4eba\u30013\u4eba\u306b\u5206\u3051\u308b<\/strong><\/p>\n<p>\u4eba\u3092\u30b0\u30eb\u30fc\u30d7\u5206\u3051\u3059\u308b\u3068\u304d\u3001\u9806\u756a\u3092\u6c17\u306b\u305b\u305a\u306b\u30b0\u30eb\u30fc\u30d7\u3078\u5165\u308c\u307e\u3059\u3002\u305d\u306e\u305f\u3081\u3001\u7d44\u307f\u5408\u308f\u305b\u306e\u516c\u5f0f\u3092\u5229\u7528\u3057\u307e\u3059\u3002\u6700\u521d\u300112\u4eba\u304b\u30895\u4eba\u3092\u9078\u3076\u306e\u3067<sub>12<\/sub>C<sub>5<\/sub>\u3067\u3059\u3002\u6b21\u306b\u6b8b\u3063\u305f7\u4eba\u304b\u30894\u4eba\u3092\u9078\u3076\u306e\u3067<sub>7<\/sub>C<sub>4<\/sub>\u3067\u3059\u3002\u306a\u304a\u3001\u6700\u5f8c\u306f3\u4eba\u306e\u4e2d\u304b\u30893\u4eba\u3092\u9078\u3076\u306e\u3067<sub>3<\/sub>C<sub>3<\/sub>\u3067\u3059\u3002\u305f\u3060\u3001<sub>3<\/sub>C<sub>3<\/sub>\u306f1\u306a\u306e\u3067\u8a08\u7b97\u3092\u7701\u304d\u307e\u3059\u3002<\/p>\n<p>\u305d\u306e\u305f\u3081\u3001\u4ee5\u4e0b\u306e\u8a08\u7b97\u5f0f\u3092\u4f5c\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<p>\\(_{12}C_5\u00d7_7C_4=\\displaystyle\\frac{12!}{5!7!}\u00d7\\displaystyle\\frac{7!}{4!3!}=27720\\)<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/03\/tuf1.jpg\" alt=\"\" width=\"599\" height=\"92\" class=\"aligncenter size-full wp-image-4934\" \/><\/p>\n<p>\u7d44\u307f\u5408\u308f\u305b\u306e\u516c\u5f0f\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u306b\u3088\u3063\u3066\u300127720\u901a\u308a\u306e\u65b9\u6cd5\u304c\u3042\u308b\u3068\u308f\u304b\u308a\u307e\u3059\u3002<\/p>\n<p><strong>(b) 4\u4eba\u305a\u3064A\u3001B\u3001C\u306e\u30b0\u30eb\u30fc\u30d7\u306b\u5206\u3051\u308b<\/strong><\/p>\n<p>\u6b21\u306b\u30014\u4eba\u305a\u3064A\u3001B\u3001C\u306e\u30b0\u30eb\u30fc\u30d7\u306b\u5206\u3051\u308b\u5834\u5408\u3092\u8003\u3048\u3066\u307f\u307e\u3057\u3087\u3046\u3002\u8003\u3048\u65b9\u306f\u5148\u307b\u3069\u3068\u540c\u3058\u3067\u3059\u3002\u6700\u521d\u300112\u4eba\u304b\u30894\u4eba\u3092\u9078\u3076\u306e\u3067<sub>12<\/sub>C<sub>4<\/sub>\u3067\u3059\u3002\u6b21\u306b\u30018\u4eba\u306e\u4e2d\u304b\u30894\u4eba\u3092\u9078\u3076\u306e\u3067<sub>8<\/sub>C<sub>4<\/sub>\u3067\u3059\u3002\u305d\u306e\u305f\u3081\u8a08\u7b97\u5f0f\u306f\u4ee5\u4e0b\u3067\u3059\u3002<\/p>\n<p>\\(_{12}C_4\u00d7_8C_4=\\displaystyle\\frac{12!}{4!8!}\u00d7\\displaystyle\\frac{8!}{4!4!}=34650\\)<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/03\/tuf2.jpg\" alt=\"\" width=\"600\" height=\"154\" class=\"aligncenter size-full wp-image-4935\" \/><\/p>\n<p><strong>(c) 4\u4eba\u305a\u3064\u30013\u3064\u306e\u30b0\u30eb\u30fc\u30d7\u306b\u5206\u3051\u308b<\/strong><\/p>\n<p>4\u4eba\u305a\u30643\u3064\u306e\u30b0\u30eb\u30fc\u30d7\u306b\u5206\u3051\u308b\u3082\u306e\u306e\u3001A\u30b0\u30eb\u30fc\u30d7\u3001B\u30b0\u30eb\u30fc\u30d7\u3001C\u3001\u30b0\u30eb\u30fc\u30d7\u306a\u3069\u306e\u533a\u5225\u304c\u306a\u3044\u30b1\u30fc\u30b9\u3067\u306e\u7d44\u307f\u5408\u308f\u305b\u3067\u3059\u3002\u3053\u306e\u5834\u5408\u3001\u5148\u307b\u3069\u306e\u8a08\u7b97\u3068\u306f\u5c11\u3057\u3084\u308a\u65b9\u304c\u7570\u306a\u308a\u307e\u3059\u3002A\u3001B\u3001C\u306e\u533a\u5225\u3092\u306a\u304f\u3059\u5834\u5408\u3001\u30b0\u30eb\u30fc\u30d7\u306e\u5206\u3051\u65b9\u306f3!\u901a\u308a\u3042\u308a\u307e\u3059\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/03\/tuf3.jpg\" alt=\"\" width=\"599\" height=\"161\" class=\"aligncenter size-full wp-image-4936\" \/><\/p>\n<p>\u305d\u3053\u3067<span style=\"color: #0000ff;\">3!\u901a\u308a\u306e\u533a\u5225\u3092\u306a\u304f\u3059\u305f\u3081\u3001(b)\u306e\u7d50\u679c\u306b\u5bfe\u3057\u30663!\u3067\u5272\u308a\u307e\u3057\u3087\u3046\u3002<\/span><\/p>\n<p>\\(\\displaystyle\\frac{34650}{3!}=5775\\)<\/p>\n<p>(a)\u306e\u8a08\u7b97\u3067\u306f\u3001\u30b0\u30eb\u30fc\u30d7\u306e\u5206\u3051\u65b9\u3092\u8003\u616e\u305b\u305a\u306b<sub>12<\/sub>C<sub>5<\/sub>\u00d7<sub>7<\/sub>C<sub>4<\/sub>\u306e\u8a08\u7b97\u3092\u3057\u307e\u3057\u305f\u3002\u3053\u306e\u7406\u7531\u3068\u3057\u3066\u306f5\u4eba\u30014\u4eba\u30013\u4eba\u306b\u5206\u3051\u308b\u304b\u3089\u3067\u3059\u30025\u4eba\u30014\u4eba\u30013\u4eba\u306e\u30b0\u30eb\u30fc\u30d7\u3067\u3042\u308c\u3070\u3001A\u30b0\u30eb\u30fc\u30d7\u3001B\u30b0\u30eb\u30fc\u30d7\u3001C\u30b0\u30eb\u30fc\u30d7\u3068\u533a\u5225\u3057\u306a\u304f\u3066\u3082\u3001\u305d\u308c\u305e\u308c\u306e\u30b0\u30eb\u30fc\u30d7\u3092\u898b\u5206\u3051\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<p>\u4e00\u65b9\u3067\u3059\u3079\u3066\u306e\u30b0\u30eb\u30fc\u30d7\u304c4\u4eba\u306e\u5834\u5408\u3001A\u30b0\u30eb\u30fc\u30d7\u3001B\u30b0\u30eb\u30fc\u30d7\u3001C\u30b0\u30eb\u30fc\u30d7\u306e\u3088\u3046\u306b\u533a\u5225\u3057\u306a\u3044\u3068\u3001\u79c1\u305f\u3061\u306f\u898b\u5206\u3051\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u305b\u3093\u3002\u4f8b\u3048\u307012\u4eba\u3092\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u5206\u3051\u308b\u3068\u304d\u3001\u4ee5\u4e0b\u306f\u3059\u3079\u3066\u540c\u3058\u7d50\u679c\u3068\u8003\u3048\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<ul>\n<li>(1-2-3-4), (5-6-7-8), (9-10-11-12)<\/li>\n<li>(5-6-7-8), (1-2-3-4), (9-10-11-12)<\/li>\n<li>(9-10-11-12), (5-6-7-8), (1-2-3-4)<\/li>\n<\/ul>\n<p>(c)\u306e\u8a08\u7b97\u3067\u306f\u30b0\u30eb\u30fc\u30d7\u3092\u533a\u5225\u3057\u306a\u3044\u305f\u3081\u3001\u305d\u306e\u5206\u3092\u8003\u616e\u3057\u30663!\u3067\u5272\u308a\u7b97\u3092\u3057\u307e\u3059\u3002<\/p>\n<p><strong>(d) 6\u4eba\u30013\u4eba\u30013\u4eba\u306e\u30b0\u30eb\u30fc\u30d7\u306b\u5206\u3051\u308b<\/strong><\/p>\n<p>\u305d\u308c\u3067\u306f\u30016\u4eba\u30013\u4eba\u30013\u4eba\u306e\u30b0\u30eb\u30fc\u30d7\u306b\u5206\u3051\u308b\u5834\u9762\u3092\u8003\u3048\u3066\u307f\u307e\u3057\u3087\u3046\u300212\u4eba\u304b\u30896\u4eba\u3092\u9078\u3076\u305f\u3081\u5f0f\u306f<sub>12<\/sub>C<sub>6<\/sub>\u3067\u3059\u3002\u6b21\u306b6\u4eba\u304b\u30893\u4eba\u3092\u9078\u3076\u306e\u3067\u5f0f\u306f<sub>6<\/sub>C<sub>3<\/sub>\u3067\u3059\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/03\/tuf4.jpg\" alt=\"\" width=\"599\" height=\"163\" class=\"aligncenter size-full wp-image-4937\" \/><\/p>\n<p>\u305f\u3060\u30013\u4eba\u306e\u30b0\u30eb\u30fc\u30d7\u304c2\u3064\u3042\u308a\u307e\u3059\u30026\u4eba\u30b0\u30eb\u30fc\u30d7\u30683\u4eba\u30b0\u30eb\u30fc\u30d7\u306b\u3064\u3044\u3066\u306f\u3001\u79c1\u305f\u3061\u306f\u898b\u5206\u3051\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u305f\u3060\u3001<span style=\"color: #0000ff;\">2\u3064\u306e3\u4eba\u30b0\u30eb\u30fc\u30d7\u306f\u898b\u5206\u3051\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u305b\u3093\u3002<\/span>\u305d\u3053\u3067\u30013\u4eba\u30b0\u30eb\u30fc\u30d7\u306e\u533a\u5225\u3092\u306a\u304f\u3059\u305f\u3081\u306b2!\u3067\u5272\u308a\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(\\displaystyle\\frac{_{12}C_6\u00d7_6C_3}{2!}=9240\\)<\/p>\n<p>\u3053\u306e\u3088\u3046\u306b\u3001\u533a\u5225\u3067\u304d\u306a\u3044\u30b0\u30eb\u30fc\u30d7\u306b\u3064\u3044\u3066\u306f\u308f\u308a\u7b97\u3092\u3059\u308b\u3053\u3068\u3067\u4f55\u901a\u308a\u306e\u30b1\u30fc\u30b9\u304c\u3042\u308b\u306e\u304b\u8a08\u7b97\u3067\u304d\u307e\u3059\u3002<\/p>\n<h2>\u540c\u3058\u3082\u306e\u3092\u542b\u3080\u9806\u5217\u306e\u8a08\u7b97<\/h2>\n<p>\u6b21\u306b\u3001\u540c\u3058\u3082\u306e\u3092\u542b\u3080\u9806\u5217\u306e\u8a08\u7b97\u3092\u3057\u3066\u307f\u307e\u3057\u3087\u3046\u3002\u5148\u307b\u3069\u8aac\u660e\u3057\u305f\u7df4\u7fd2\u554f\u984c\u3092\u89e3\u3051\u308b\u5834\u5408\u3001\u540c\u3058\u3082\u306e\u3092\u542b\u3080\u9806\u5217\u306e\u8a08\u7b97\u306f\u7c21\u5358\u3067\u3059\u3002<\/p>\n<p>\u4e00\u822c\u7684\u306a\u9806\u5217\u3067\u306f\u3001\u5de6\u304b\u3089\u9806\u306b\u4e26\u3079\u308b\u3068\u304d\u3001\u3059\u3079\u3066\u306e\u8981\u7d20\u3092\u898b\u5206\u3051\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u305d\u306e\u305f\u3081\u968e\u4e57\u3084\u9806\u5217\u306e\u516c\u5f0f\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u306b\u3088\u3063\u3066\u7b54\u3048\u3092\u51fa\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u4e00\u65b9\u3001\u4ee5\u4e0b\u306e8\u500b\u306e\u3088\u3046\u306b\u5b9d\u77f3\u3092\u4e26\u3079\u308b\u3068\u304d\u3001\u3069\u306e\u3088\u3046\u306b\u8003\u3048\u308c\u3070\u3044\u3044\u3067\u3057\u3087\u3046\u304b\uff08\u540c\u3058\u8272\u306e\u5b9d\u77f3\u306f\u898b\u5206\u3051\u308b\u3053\u3068\u304c\u3067\u304d\u306a\u3044\u3068\u3059\u308b\uff09\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/03\/tuf5.jpg\" alt=\"\" width=\"600\" height=\"64\" class=\"aligncenter size-full wp-image-4938\" \/><\/p>\n<p>\u8272\u304c\u9055\u3046\u5834\u5408\u3001\u5b9d\u77f3\u3092\u898b\u5206\u3051\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u305f\u3060\u8272\u304c\u540c\u3058\u5b9d\u77f3\u306b\u3064\u3044\u3066\u306f\u3001\u79c1\u305f\u3061\u306f\u898b\u5206\u3051\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u305b\u3093\u3002<\/p>\n<p>\u5148\u307b\u3069\u3001\u533a\u5225\u3067\u304d\u306a\u3044\u8981\u7d20\u306b\u3064\u3044\u3066\u306f\u3001\u5272\u308a\u7b97\u3092\u3059\u308b\u3053\u3068\u306b\u3088\u3063\u3066\u7d50\u679c\u304b\u3089\u7701\u304b\u306a\u3051\u308c\u3070\u3044\u3051\u306a\u3044\u3053\u3068\u3092\u89e3\u8aac\u3057\u307e\u3057\u305f\u3002\u4eca\u56de\u306e\u8a08\u7b97\u306b\u3064\u3044\u3066\u3082\u3001<span style=\"color: #0000ff;\">\u540c\u3058\u3082\u306e\u306b\u3064\u3044\u3066\u5272\u308a\u7b97\u3092\u3059\u308b\u3053\u3068\u306b\u3088\u3063\u3066\u7701\u304f\u3088\u3046\u306b\u3057\u307e\u3057\u3087\u3046\u3002<\/span><\/p>\n<p>8\u500b\u306e\u5b9d\u77f3\u3092\u5de6\u304b\u3089\u9806\u306b\u4e26\u3079\u308b\u3068\u304d\u30018!\u901a\u308a\u306e\u65b9\u6cd5\u304c\u3042\u308a\u307e\u3059\u3002\u305d\u306e\u5f8c\u3001\u898b\u5206\u3051\u308b\u3053\u3068\u304c\u3067\u304d\u306a\u3044\u8981\u7d20\u3092\u5272\u308a\u7b97\u3057\u307e\u3057\u3087\u3046\u3002\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8003\u3048\u307e\u3059\u3002<\/p>\n<p>\\(\\displaystyle\\frac{8!}{2!2!3!1!}=1680\\)<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/03\/tuf6.jpg\" alt=\"\" width=\"599\" height=\"204\" class=\"aligncenter size-full wp-image-4939\" \/><\/p>\n<p>\u3053\u306e\u3088\u3046\u306b\u3001\u898b\u5206\u3051\u308b\u3053\u3068\u304c\u3067\u304d\u306a\u3044\u8981\u7d20\u306b\u3064\u3044\u3066\u9806\u5217\u3092\u8a08\u7b97\u3057\u3001\u5272\u308a\u7b97\u3092\u3057\u307e\u3059\u3002\u3053\u308c\u306b\u3088\u3063\u3066\u3001\u540c\u3058\u3082\u306e\u3092\u542b\u3080\u9806\u5217\u3092\u8a08\u7b97\u3067\u304d\u307e\u3059\u3002<\/p>\n<h3>\u540c\u3058\u3082\u306e\u3092\u542b\u3080\u9806\u5217\u306b\u306f2\u901a\u308a\u306e\u89e3\u7b54\u6cd5\u304c\u3042\u308b<\/h3>\n<p>\u306a\u304a\u3001\u540c\u3058\u3082\u306e\u3092\u542b\u3080\u9806\u5217\u306b\u306f\u4ed6\u306b\u3082\u89e3\u7b54\u65b9\u6cd5\u304c\u3042\u308a\u307e\u3059\u3002\u305d\u3053\u3067\u3001\u6b21\u306f\u7d44\u307f\u5408\u308f\u305b\u306e\u516c\u5f0f\u3092\u5229\u7528\u3057\u3066\u5148\u307b\u3069\u306e\u554f\u984c\u3092\u89e3\u3044\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\u5b9d\u77f3\u30928\u500b\u4e26\u3079\u308b\u3068\u304d\u3001\u540c\u3058\u8272\u3092\u533a\u5225\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u305b\u3093\u3002\u305d\u306e\u305f\u3081\u3001\u4f8b\u3048\u3070\u7dd1\u306e\u5b9d\u77f3\u3092\u7f6e\u304f\u3068\u304d\u3001\u300c8\u500b\u306e\u4e2d\u304b\u30892\u500b\u3092\u9078\u3079\u3070\u3044\u3044\u300d\u3068\u8003\u3048\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u305d\u306e\u305f\u3081\u5f0f\u306f<sub>8<\/sub>C<sub>2<\/sub>\u3067\u3059\u3002<\/p>\n<p>\u6b21\u306b\u9752\u306e\u5b9d\u77f3\u3092\u7f6e\u304f\u3068\u304d\u3001\u6b8b\u308a\u306e6\u500b\u306e\u4e2d\u304b\u30892\u500b\u3092\u9078\u3076\u306e\u3067\u5f0f\u306f<sub>6<\/sub>C<sub>2<\/sub>\u3067\u3059\u3002\u307e\u305f\u8d64\u8272\u306e\u5b9d\u77f3\u3092\u7f6e\u304f\u3068\u304d\u3001\u6b8b\u308a\u306e4\u500b\u306e\u4e2d\u304b\u30893\u500b\u3092\u9078\u3076\u306e\u3067<sub>4<\/sub>C<sub>3<\/sub>\u3067\u3059\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/03\/tuf7.jpg\" alt=\"\" width=\"600\" height=\"179\" class=\"aligncenter size-full wp-image-4940\" \/><\/p>\n<p>\u305d\u3053\u3067\u3001\u4ee5\u4e0b\u306e\u8a08\u7b97\u3092\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(_8C_2\u00d7_6C_2\u00d7_4C_3=1680\\)<\/p>\n<p>\u3053\u3046\u3057\u3066\u3001\u5148\u307b\u3069\u3068\u540c\u3058\u7b54\u3048\u3092\u51fa\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u3069\u3061\u3089\u306e\u65b9\u6cd5\u3082\u6b63\u89e3\u3067\u3042\u308a\u3001\u540c\u3058\u3082\u306e\u3092\u542b\u3080\u9806\u5217\u3067\u306f2\u901a\u308a\u306e\u89e3\u304d\u65b9\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n<h2>\u91cd\u8907\u7d44\u307f\u5408\u308f\u305b\u306e\u8a08\u7b97\u65b9\u6cd5<\/h2>\n<p>\u7d44\u307f\u5408\u308f\u305b\u306e\u554f\u984c\u3067\u306f\u3001\u300c\u4f55\u5ea6\u3082\u540c\u3058\u8981\u7d20\u3092\u5229\u7528\u3067\u304d\u308b\u7d44\u307f\u5408\u308f\u305b\u300d\u304c\u3042\u308a\u307e\u3059\u3002\u901a\u5e38\u3001\u7d44\u307f\u5408\u308f\u305b\u3067\u306f\u4e00\u56de\u3060\u3051\u9078\u3076\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u4f8b\u3048\u3070\u30018\u4eba\u306e\u4e2d\u304b\u30894\u4eba\u3092\u9078\u3076\u3068\u304d\u3001\u8a08\u7b97\u5f0f\u306f<sub>8<\/sub>C<sub>4<\/sub>\u3067\u3059\u3002\u5206\u8eab\u3067\u304d\u308b\u5834\u5408\u3092\u9664\u304d\u3001\u540c\u3058\u4eba\u9593\u3092\u4e00\u5ea6\u306b\u4e8c\u56de\u9078\u3076\u3053\u3068\u306f\u3067\u304d\u307e\u305b\u3093\u3002<\/p>\n<p>\u305f\u3060<span style=\"color: #ff0000;\">\u7269\u3092\u9078\u3076\u3068\u304d\u3067\u3042\u308c\u3070\u3001\u540c\u3058\u3082\u306e\u3092\u91cd\u8907\u3057\u3066\u9078\u3079\u308b\u30b1\u30fc\u30b9\u304c\u3042\u308a\u307e\u3059\u3002<\/span>\u4f8b\u3048\u3070\u3001\u4ee5\u4e0b\u306e\u72b6\u6cc1\u3092\u8003\u3048\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/p>\n<ul>\n<li>\u307f\u304b\u3093\u3001\u30ea\u30f3\u30b4\u3001\u30d0\u30ca\u30ca\u306b\u3064\u3044\u3066\u3001\u5408\u8a088\u500b\u3092\u8cb7\u3046\u3068\u304d\u3001\u4f55\u901a\u308a\u306e\u65b9\u6cd5\u304c\u3042\u308a\u307e\u3059\u304b\uff08\u4e00\u3064\u3082\u8cb7\u308f\u306a\u3044\u679c\u7269\u304c\u3042\u3063\u3066\u3082\u3044\u3044\uff09<\/li>\n<\/ul>\n<p>\u4f8b\u3048\u3070\u307f\u304b\u3093\u30926\u500b\u8cb7\u3046\u5834\u5408\u3001\u540c\u3058\u3082\u306e\uff08\u307f\u304b\u3093\uff09\u3092\u91cd\u8907\u3057\u30666\u500b\u8cb7\u3046\u3053\u3068\u306b\u306a\u308a\u307e\u3059\u3002\u30ea\u30f3\u30b4\u30922\u500b\u8cb7\u3046\u5834\u5408\u3001\u540c\u3058\u3082\u306e\uff08\u30ea\u30f3\u30b4\uff09\u3092\u91cd\u8907\u3057\u30662\u500b\u8cb7\u3046\u3053\u3068\u306b\u306a\u308a\u307e\u3059\u3002\u307f\u304b\u3093\u3084\u30ea\u30f3\u30b4\u3001\u30d0\u30ca\u30ca\u304c\u5e97\u306b\u305f\u304f\u3055\u3093\u7f6e\u304b\u308c\u3066\u3044\u308b\u5834\u5408\u3001\u4f55\u500b\u3067\u3082\u8cb7\u3046\u3053\u3068\u304c\u3067\u304d\u308b\u306e\u3067\u3059\u3002<\/p>\n<p>\u306a\u304a\u91cd\u8907\u7d44\u307f\u5408\u308f\u305b\u306e\u554f\u984c\u3092\u89e3\u304f\u5834\u5408\u3001\u8003\u3048\u65b9\u304c\u7279\u6b8a\u3067\u3059\u3002\u5177\u4f53\u7684\u306b\u306f\u3001<span style=\"color: #ff0000;\">\u533a\u5207\u308a\uff08|\uff09\u3092\u5229\u7528\u3057\u3066\u554f\u984c\u3092\u89e3\u304d\u307e\u3057\u3087\u3046\u3002<\/span>\u5148\u307b\u3069\u306e\u554f\u984c\u3067\u3042\u308c\u3070\u3001\u5408\u8a08\u30678\u500b\u306e\u679c\u7269\u3092\u8cb7\u3044\u307e\u3059\u3002\u305d\u3053\u3067\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b8\u500b\u306e\u3007\u3092\u4f5c\u308a\u307e\u3057\u3087\u3046\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/03\/tuf8.jpg\" alt=\"\" width=\"600\" height=\"65\" class=\"aligncenter size-full wp-image-4941\" \/><\/p>\n<p>\u6b21\u306b\u3001\u4ed5\u5207\u308a\u30922\u3064\u52a0\u3048\u307e\u3059\u3002<span style=\"color: #0000ff;\">\u4ed5\u5207\u308a\u304c2\u3064\u3042\u308c\u3070\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u533a\u5207\u308b\u5834\u6240\u306b\u3088\u3063\u3066\u307f\u304b\u3093\u3001\u30ea\u30f3\u30b4\u3001\u30d0\u30ca\u30ca\u3092\u8cb7\u3046\u500b\u6570\u3092\u5206\u3051\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/span><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/03\/tuf13.jpg\" alt=\"\" width=\"600\" height=\"222\" class=\"aligncenter size-full wp-image-4942\" \/><\/p>\n<p>\u4e38\u306f8\u3064\u3067\u3042\u308a\u3001\u4ed5\u5207\u308a\u306f2\u500b\u3067\u3059\u3002\u305d\u306e\u305f\u3081\u300c10\u500b\u306e\u5834\u6240\u304b\u3089\u30012\u30f6\u6240\u306e\u4ed5\u5207\u308a\u3092\u7f6e\u304f\u5834\u6240\u3092\u9078\u3079\u3070\u3044\u3044\u300d\u3068\u8003\u3048\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u3064\u307e\u308a\u3001\u8a08\u7b97\u5f0f\u306f\u4ee5\u4e0b\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>\\(_{10}C_2=45\\)<\/p>\n<p>\u91cd\u8907\u7d44\u307f\u5408\u308f\u305b\u306e\u8003\u3048\u65b9\u306f\u7279\u6b8a\u3067\u3042\u308a\u3001\u89e3\u304d\u65b9\u3092\u7406\u89e3\u3057\u3066\u3044\u306a\u3044\u3068\u7b54\u3048\u3092\u51fa\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u305b\u3093\u3002\u306a\u304a\u5148\u307b\u3069\u306e\u554f\u984c\u306b\u3064\u3044\u3066\u30014\u7a2e\u985e\u306e\u679c\u7269\uff08\u307f\u304b\u3093\u3001\u30ea\u30f3\u30b4\u3001\u30d0\u30ca\u30ca\u3001\u3076\u3069\u3046\uff09\u3092\u5408\u8a088\u500b\u8cb7\u3046\u3068\u304d\u3067\u306f\u3001\u3007\u304c8\u3064\u3067\u3042\u308a\u3001\u4ed5\u5207\u308a\u304c3\u3064\u5fc5\u8981\u306b\u306a\u308b\u306e\u3067\u4ee5\u4e0b\u306e\u8a08\u7b97\u5f0f\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>\\(_{11}C_3=165\\)<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/03\/tuf15.jpg\" alt=\"\" width=\"600\" height=\"214\" class=\"aligncenter size-full wp-image-4943\" \/><\/p>\n<p>3\u3064\u306b\u5206\u3051\u308b\u5834\u5408\u3001\u4ed5\u5207\u308a\u306f2\u3064\u5fc5\u8981\u3067\u3059\u3002\u307e\u305f4\u3064\u306b\u5206\u3051\u308b\u5834\u5408\u3001\u4ed5\u5207\u308a\u306f3\u3064\u5fc5\u8981\u3067\u3059\u3002\u5206\u3051\u308b\u6570\u304b\u30891\u3092\u5f15\u304f\u3068\u3001\u5fc5\u8981\u306a\u4ed5\u5207\u308a\u306e\u6570\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>\u306a\u304a\u91cd\u8907\u7d44\u307f\u5408\u308f\u305b\u3067\u306f\u3001n\u500b\u304b\u3089\u91cd\u8907\u3092\u8a31\u3057\u3066r\u500b\u3092\u53d6\u308a\u51fa\u3059\u5834\u5408\u3001\u4ee5\u4e0b\u306e\u516c\u5f0f\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(_nH_r=_{n+r-1}C_r\\)<\/li>\n<\/ul>\n<p>\u3053\u306e\u516c\u5f0f\u3092\u899a\u3048\u3066\u3082\u3044\u3044\u3067\u3059\u304c\u3001\u610f\u5473\u3092\u7406\u89e3\u3057\u3066\u3044\u306a\u3044\u3068\u5229\u7528\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u305b\u3093\u3002\u305d\u3053\u3067\u3001\u4e38\u3068\u4ed5\u5207\u308a\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u306b\u3088\u3063\u3066\u91cd\u8907\u7d44\u307f\u5408\u308f\u305b\u306e\u7b54\u3048\u3092\u51fa\u3059\u3088\u3046\u306b\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<h3>\u5fc5\u305a\u4e00\u3064\u306f\u9078\u3070\u306a\u3044\u3068\u3044\u3051\u306a\u3044\u5834\u5408\u306e\u91cd\u8907\u7d44\u307f\u5408\u308f\u305b\u306e\u89e3\u7b54\u65b9\u6cd5<\/h3>\n<p>\u5148\u307b\u3069\u3001\u4e00\u3064\u3082\u9078\u3070\u306a\u3044\u679c\u7269\u304c\u3042\u3063\u3066\u3082\u554f\u984c\u306a\u3044\u30b1\u30fc\u30b9\u3067\u91cd\u8907\u7d44\u307f\u5408\u308f\u305b\u3092\u8003\u3048\u307e\u3057\u305f\u3002\u305d\u308c\u3067\u306f\u3001\u4ee5\u4e0b\u306e\u30b1\u30fc\u30b9\u3067\u306f\u3069\u306e\u3088\u3046\u306b\u8003\u3048\u308c\u3070\u3044\u3044\u3067\u3057\u3087\u3046\u304b\u3002<\/p>\n<ul>\n<li>\u307f\u304b\u3093\u3001\u30ea\u30f3\u30b4\u3001\u30d0\u30ca\u30ca\u306b\u3064\u3044\u3066\u3001\u5408\u8a088\u500b\u3092\u8cb7\u3046\u3068\u304d\u3001\u4f55\u901a\u308a\u306e\u65b9\u6cd5\u304c\u3042\u308a\u307e\u3059\u304b\uff08\u3069\u306e\u679c\u7269\u3082\u5c11\u306a\u304f\u3068\u30821\u500b\u306f\u8cb7\u3046\uff09<\/li>\n<\/ul>\n<p>\u3053\u306e\u5834\u5408\u3082\u540c\u3058\u3088\u3046\u306b\u3001\u533a\u5207\u308a\u3092\u5229\u7528\u3057\u3066\u554f\u984c\u3092\u89e3\u304d\u307e\u3059\u3002\u5fc5\u8981\u306a\u533a\u5207\u308a\u306f2\u3064\u3067\u3059\u3002\u305f\u3060\u5c11\u306a\u304f\u3068\u3082\u3001\u307f\u304b\u30931\u500b\u3001\u30ea\u30f3\u30b41\u500b\u3001\u30d0\u30ca\u30ca1\u500b\u306f\u5fc5\u305a\u8cb7\u308f\u306a\u3051\u308c\u3070\u3044\u3051\u307e\u305b\u3093\u30028\u500b\u3092\u8cb7\u3046\u4e2d\u3067\u30013\u500b\u306f\u3059\u3067\u306b\u6c7a\u307e\u3063\u3066\u3044\u307e\u3059\u3002\u305d\u306e\u305f\u3081\u3001\u3053\u306e3\u3064\u306b\u3064\u3044\u3066\u306f\u9664\u5916\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\u305d\u3046\u3057\u3066\u6b8b\u3063\u305f5\u3064\u306b\u3064\u3044\u3066\u3001\u4ed5\u5207\u308a2\u3064\u3092\u5229\u7528\u3057\u3066\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u5206\u3051\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/03\/tuf11.jpg\" alt=\"\" width=\"599\" height=\"310\" class=\"aligncenter size-full wp-image-4944\" \/><\/p>\n<p>\u9078\u3076\u5019\u88dc\u304c5\u3064\u3001\u4ed5\u5207\u308a\u304c2\u3064\u3067\u3042\u308b\u305f\u3081\u3001\u4ee5\u4e0b\u306e\u8a08\u7b97\u5f0f\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>\\(_7C_2=21\\)<\/p>\n<p><span style=\"color: #0000ff;\">1\u3064\u4ee5\u4e0a\u3092\u9078\u3076\u91cd\u8907\u9806\u5217\u3067\u306f\u3001\u4f55\u500b\u3092\u5148\u306b\u9078\u3076\u306e\u304b\u306b\u3088\u3063\u3066\u5f15\u304d\u7b97\u3092\u3059\u308b\u6570\u3092\u6c7a\u3081\u307e\u3057\u3087\u3046\u3002<\/span>\u4eca\u56de\u3067\u306f\u3001\u8cb7\u3046\u5408\u8a08\u6570\uff088\u500b\uff09\u306e\u3046\u30613\u500b\uff08\u30df\u30ab\u30f31\u500b\u3001\u30ea\u30f3\u30b41\u500b\u3001\u30d0\u30ca\u30ca1\u500b\uff09\u3092\u8cb7\u3046\u3068\u65e2\u306b\u6c7a\u307e\u3063\u3066\u3044\u308b\u305f\u3081\u30013\u3092\u5f15\u304d\u307e\u3059\u3002<\/p>\n<p>\u305d\u306e\u305f\u3081\u3001\u4f8b\u3048\u3070<span>4<\/span>\u500b\uff08\u5c11\u306a\u304f\u3068\u3082\u30df\u30ab\u30f32\u500b\u3001\u30ea\u30f3\u30b41\u500b\u3001\u30d0\u30ca\u30ca1\u500b\uff09\u3092\u8cb7\u3046\u3068\u65e2\u306b\u6c7a\u307e\u3063\u3066\u3044\u308b\u5834\u5408\u30014\u3092\u5f15\u304d\u307e\u3059\u3002\u3064\u307e\u308a\u9078\u3079\u308b\u5019\u88dc\u306f4\u3064\u3067\u3042\u308a\u3001\u4ed5\u5207\u308a\u306f2\u3064\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/03\/tuf12.jpg\" alt=\"\" width=\"599\" height=\"58\" class=\"aligncenter size-full wp-image-4945\" \/><\/p>\n<p>\u305d\u306e\u305f\u3081\u3001\u4ee5\u4e0b\u306e\u8a08\u7b97\u5f0f\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>\\(_6C_2=15\\)<\/p>\n<p>\u4ed5\u5207\u308a\u3092\u5229\u7528\u3059\u308c\u3070\u3001\u91cd\u8907\u7d44\u307f\u5408\u308f\u305b\u306e\u7b54\u3048\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u4f8b\u3048\u3070\u3001\u4ee5\u4e0b\u306e\u7b54\u3048\u306f\u4f55\u3067\u3057\u3087\u3046\u304b\u3002<\/p>\n<ul>\n<li>\\(x+y+z=8\\)\u3067\u3042\u308a\u3001\\(x\u22670\\), \\(y\u22670\\), \\(z\u22670\\)\u306e\u6574\u6570\u306b\u3064\u3044\u3066\u3001\\(x,y,z\\)\u306e\u7d44\u307f\u5408\u308f\u305b\u306f\u4f55\u901a\u308a\u3067\u3057\u3087\u3046\u304b<\/li>\n<\/ul>\n<p>\\(x\\)\u3084\\(y\\)\u3001\\(z\\)\u306f\u4f55\u5ea6\u9078\u3093\u3067\u3082\u3044\u3044\u3067\u3059\u3002\u305d\u306e\u305f\u3081\u91cd\u8907\u7d44\u307f\u5408\u308f\u305b\u3067\u3042\u308a\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b2\u3064\u306e\u4ed5\u5207\u308a\u3092\u5229\u7528\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/03\/tuf16.jpg\" alt=\"\" width=\"598\" height=\"466\" class=\"aligncenter size-full wp-image-4946\" 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