HMMT 二月 2007 · 冲刺赛 · 第 2 题
HMMT February 2007 — Guts Round — Problem 2
题目详情
- [ 5 ] A candy company makes 5 colors of jellybeans, which come in equal proportions. If I grab a random sample of 5 jellybeans, what is the probability that I get exactly 2 distinct colors? 2
解析
- [ 5 ] A candy company makes 5 colors of jellybeans, which come in equal proportions. If I grab a random sample of 5 jellybeans, what is the probability that I get exactly 2 distinct colors? ( ) 5 12 5 Answer: . There are = 10 possible pairs of colors. Each pair of colors contributes 2 − 2 = 30 125 2 5 sequences of beans that use both colors. Thus, the answer is 10 · 30 / 5 = 12 / 125. 2