有7个同学排成一排照相,问:1、一共有多少种排法?2、如果某人不坐在前端,一共有多少种排法?

2025-04-02 10:58:01
推荐回答(3个)
回答1:

1)7个人占据7个位置,有排法7×6×5×4×3×2×1=5040 种。
2)某人不坐在前端,意思有点不明白,是否为两端?
如果是两端,则此人的位置可能有5种,其余6人占据剩余6个位置,
有排法 5×6×5×4×3×2×1=3600 种。
如果只是一端,则此人的位置可能有6种,其余6人占据剩余6个位置,
有排法 6×6×5×4×3×2×1=4320 种。
3)甲必须站在正中间,则甲只有1种,其余6人占据剩余6个位置,
有排法 1×6×5×4×3×2×1=720 种。
4)甲、乙两人必须站在两端,则甲乙有2种,其余5人占据剩余5个位置,
有排法 2×5×4×3×2×1=240 种。

回答2:

(1)7*6*5*4*3*2*1=5040种 (A77,前一个7是下标,后一个7是上标,下面均同)
(2)6*6*5*4*3*2*1=4320种 (A61*A66)
(3)甲站中间是简单的排列问题 有A66种
(4)甲乙站一起利用捆绑法 分两步 第一步甲乙捆绑有A22种 第二步将甲乙整体和其余五个元素排列
有A55种 所以共有 A22乘以A55种

回答3:

[1]5040.....[2,]4320.....[.3,]720....[.4],240

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