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赵鑫 2024-01-21 19:44:14 +08:00
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概念/排列与组合.md
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@ -12,4 +12,4 @@ $$ A_{10}^3 = \underbrace{10\times9\times8}_{3个} = 720 $$
$$ A_n^n = \underbrace{n\times(n-1)\times(n-2)\times\cdots\times1}_{n个} = n! （A_n^n叫全排列，n!叫做n的阶乘） $$ $$ A_n^n = \underbrace{n\times(n-1)\times(n-2)\times\cdots\times1}_{n个} = n! （A_n^n叫全排列，n!叫做n的阶乘） $$
$$ A_{n}^{m} = \underbrace{n\times(n-1)\times(n-2)\times\cdots\times(n-m+1)}_{m个} = \dfrac{n\times(n-1)\times(n-2)\times\cdots\times(n-m+1)\times(n-m)\times(n-m-1)\times(n-m-2)\times\cdots\times1}{(n-m)\times(n-m-1)\times(n-m-2)\times\cdots\times1} = \dfrac{n!}{(n-m)!}$$ $$ A_{n}^{m} = \underbrace{n\times(n-1)\times(n-2)\times\cdots\times(n-m+1)}_{m个} \\\\ = \dfrac{n\times(n-1)\times(n-2)\times\cdots\times(n-m+1)\times(n-m)\times(n-m-1)\times(n-m-2)\times\cdots\times1}{(n-m)\times(n-m-1)\times(n-m-2)\times\cdots\times1} \\\\ = \dfrac{n!}{(n-m)!}$$