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HMMT 二月 2001 · 冲刺赛 · 第 20 题

HMMT February 2001 — Guts Round — Problem 20

专题
Contest Math / 竞赛数学
难度
L3
来源
HMMT

题目详情

英文原题

  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 possibleconfiguration having an equal probability, what is the probability that exactly six of theletters are in the correct envelopes?
    ∞
    ∑
    ( i +1)( i +2)( i +3)
解析

英文解析

  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 possibleconfiguration having an equal probability, what is the probability that exactly six of theletters 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)