From aa85ea96a75161f9a5631e3807c983cd51535544 Mon Sep 17 00:00:00 2001 From: Zhao Xin <7176466@qq.com> Date: Sun, 21 Jan 2024 19:55:27 +0800 Subject: [PATCH] =?UTF-8?q?=E6=9B=B4=E6=96=B0?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- 概念/排列与组合.md | 2 ++ 1 file changed, 2 insertions(+) diff --git a/概念/排列与组合.md b/概念/排列与组合.md index 1f0db51..0ee839a 100644 --- a/概念/排列与组合.md +++ b/概念/排列与组合.md @@ -9,3 +9,5 @@ 从10人中选出第1名有10种可能,从剩下的10-1=9人中选出第2名有9种可能,再从剩下的9-1=8人中选出第3名有8种可能,这三步的可能数用**乘法原理**相乘,$10\times9\times8=720$ 即总的排列数。排列数可写作: $$ \begin{align} A_{10}^3 &= \underbrace{10\times9\times8}_{3个} = 720 \newline A_n^n &= \underbrace{n\times(n-1)\times(n-2)\times\cdots\times1}_{n个} = n! (A_n^n叫全排列,n!叫做n的阶乘) \newline A_{n}^{m} &= \underbrace{n\times(n-1)\times(n-2)\times\cdots\times(n-m+1)}_{m个} \newline &= \dfrac{n\times(n-1)\times(n-2)\times\cdots\times(n-m+1)\times(n-m)\times(n-m-1)\times(n-m-2)\times\cdots\times1}{(n-m)\times(n-m-1)\times(n-m-2)\times\cdots\times1} \newline &= \dfrac{n!}{(n-m)!} \end{align}$$ + +公式1:$ A_n^n = n! $