返回题库

HMMT 二月 2001 · 冲刺赛 · 第 20 题

HMMT February 2001 — Guts Round — Problem 20

专题
Discrete Math / 离散数学
难度
L3
来源
HMMT

题目详情

  1. [ ± 4] Karen has seven envelopes and seven letters of congratulations to various HMMT coaches. If she places the letters in the envelopes at random with each possible configuration having an equal probability, what is the probability that exactly six of the letters are in the correct envelopes? ∞ ∑ ( i +1)( i +2)( i +3)
解析
  1. [ ± 4] Karen has seven envelopes and seven letters of congratulations to various HMMT coaches. If she places the letters in the envelopes at random with each possible configuration having an equal probability, what is the probability that exactly six of the letters are in the correct envelopes? Solution: 0 , since if six letters are in their correct envelopes the seventh is as well. ∞ ∑ ( i +1)( i +2)( i +3)