Question

A committee of 4 people is randomly selected from a group of 5 Republicans and 6 Democrats. What is the probability that the committee will be only Democrats?

Answer 1

We have 5 Republican Candidates and 6 Democratic Candidates

We have a total 11 candidates to choose from

First pick of Democratic Candidates = 6/11
Second pick of Democratic Candidates = 5/10
Third pick of Democratic Candidates = 4/9
Fourth pick of Democratic Candidates = 3/8

The probability of four Democratic candidates in the committee is
$\frac{6}{11}$×$\frac{5}{10}$×$\frac{4}{9}$×$\frac{3}{8}$ = $\frac{360}{7920} = \frac{1}{22}$