返回题库

HMMT 二月 2007 · 冲刺赛 · 第 2 题

HMMT February 2007 — Guts Round — Problem 2

专题
Contest Math / 竞赛数学
难度
L3
来源
HMMT

题目详情

英文原题

  1. [ 5 ] A candy company makes 5 colors of jellybeans, which come in equal proportions. If I grab a randomsample of 5 jellybeans, what is the probability that I get exactly 2 distinct colors? 2
解析

英文解析

  1. [ 5 ] A candy company makes 5 colors of jellybeans, which come in equal proportions. If I grab a randomsample of 5 jellybeans, what is the probability that I get exactly 2 distinct colors?
    ( )
    5125
    Answer: . There are = 10 possible pairs of colors. Each pair of colors contributes 2 − 2 = 30
    125 2
    sequences of beans that use both colors. Thus, the answer is 10 · 30 / 5 = 12 / 125.5 2