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赵鑫 2024-01-21 19:52:28 +08:00
parent 5501b21682
commit 9cabfc3a98

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@ -12,4 +12,4 @@ $$ A_{10}^3 = \underbrace{10\times9\times8}_{3个} = 720 $$
$$ A_n^n = \underbrace{n\times(n-1)\times(n-2)\times\cdots\times1}_{n个} = n! A_n^n叫全排列n!叫做n的阶乘 $$
$$ \begin{align} A_{n}^{m} &= \underbrace{n\times(n-1)\times(n-2)\times\cdots\times(n-m+1)}_{m个} \\ &= \dfrac{n\times(n-1)\times(n-2)\times\cdots\times(n-m+1)\times(n-m)\times(n-m-1)\times(n-m-2)\times\cdots\times1}{(n-m)\times(n-m-1)\times(n-m-2)\times\cdots\times1} \\ &= \dfrac{n!}{(n-m)!} \end{align}$$
$$ \begin{align} A_{n}^{m} &= \underbrace{n\times(n-1)\times(n-2)\times\cdots\times(n-m+1)}_{m个} \newline &= \dfrac{n\times(n-1)\times(n-2)\times\cdots\times(n-m+1)\times(n-m)\times(n-m-1)\times(n-m-2)\times\cdots\times1}{(n-m)\times(n-m-1)\times(n-m-2)\times\cdots\times1} \newline &= \dfrac{n!}{(n-m)!} \end{align}$$