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