A city council consists of seven Democrats and seven Republicans. If a committee of five people is selected, find the probability of selecting two Democrats and three Republicans.

Answer 1

This problem requires a simple application of the hypergeometric distribution.

_nC_r is the binomial coefficient of n things taken r at a time

Your probability is given by ₇C₂ * ₇C₃ / ₁₄C_5.