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HMMT 十一月 2012 · 冲刺赛 · 第 8 题

HMMT November 2012 — Guts Round — Problem 8

专题
Contest Math / 竞赛数学
难度
L3
来源
HMMT

题目详情

英文原题

  1. [ 7 ] Three cards are drawn from the top of a shuffled standard 52-card deck. Find the probability that they are all of different suits. (A suit is either spades, clubs, hearts, or diamonds.)
解析

英文解析

  1. [ 7 ]
    Answer: There are 13 cards of each suit. The probability that the second card has a different 169
    3 · 13425
    suit than the first is . The probability that the third card has a different suit than the first and
    52 − 1
    2 · 13
    second card is
    52 − 2
    Since the two events need to both occur, we use the multiplicative rule:
    3 · 13 2 · 13
    ·
    52 − 1 52 − 2 =169
    425