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HMMT 二月 2005 · GEN2 赛 · 第 4 题

HMMT February 2005 — GEN2 Round — Problem 4

专题
Contest Math / 竞赛数学
难度
L3
来源
HMMT

题目详情

英文原题

  1. In how many ways can 8 people be arranged in a line if Alice and Bob must be nextto each other, and Carol must be somewhere behind Dan?
解析

英文解析

  1. In how many ways can 8 people be arranged in a line if Alice and Bob must be nextto each other, and Carol must be somewhere behind Dan?
    Solution: 5040
    Let us place Alice and Bob as a single person; there are then 7! = 5040 differentarrangements. Alice can be in front of Bob or vice versa, multiplying the number ofpossibilities by 2, but Carol is behind Dan in exactly half of those, so that the answeris just 5040.