問題の解答
検索用コード（LaTeX）
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% 例題A1.2.9：平面の色分け（One More）★
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右のそれぞれの図において，分けられた領域を互いに異なる4色すべてを用いて塗り分ける方法は何通りあるか．ただし，同じ色を複数回用いることはできるが，隣り合う領域は異なる色で塗るものとする．
(1)
(2)
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% 例題A1.2.9の解答（One More）★
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(1) 領域は4箇所あるから，4色すべてを用いて塗る場合の数は，
\[
{}_4\mathrm{P}_4=4!=24(\text{通り})
\]
(2) 領域は5箇所あるから，4色を用いて塗るとき，2箇所は同じ色を使う．
同じ色を用いる2箇所の組は，(ii)と(iv)，(iii)と(v)の2通り
同じ色を塗る2箇所をまとめて1箇所として考えると，残りの3箇所を合わせた4箇所に4色を塗るから，その塗り方は${}_4\mathrm{P}_4$通り
よって，$2\times 4!=48(\text{通り})$
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% 問題A1.2.9：平面の色分け（One More）★
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右の図において，分けられた領域を互いに異なる5色すべてを用いて塗り分ける方法は何通りあるか．
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% 問題A1.2.9の解答（One More）★
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領域は5箇所あるから，5色すべてを用いて塗る場合の数は，
\[
{}_5\mathrm{P}_5=5!=120(\text{通り})
\]
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