HMMT 二月 2000 · ADV 赛 · 第 6 题
HMMT February 2000 — ADV Round — Problem 6
题目详情
英文原题
- 6 p eople each have a hat. If they sh u e their hats and redistribute them, what is theprobabilit y that exa tly one p erson gets their o wn hat ba k?
p pa b 3
2 2 2 2
解析
英文解析
- There are 6 p eople that ould get their hat ba k, so we m ust m ultiply 6 b y the n um b erof w a ys that the other 5 p eople an arrange their hats such that no one gets his/her hatba k. So, the number of w a ys this will happ en is (6 derangemen t of 5), or 6 44 = 264.
Sin e there are 6! = 720 p ossible arrangemen ts of hats, the probabilit y of exa tly one
26411
p erson getting their hat ba k is = .
30720