Probability on committee making

Question

A committee of 5 people is to be formed randomly from a group of 10 women and 5 men, what is the probability that the committee has at least 2 men?

Answer 1

Well we can choose the committee in 15 C 5 ways.

How many of these have at least two men.

Well number of ways with no men, 10 C 5 (we just choose from women)

Number of ways with 1 man : 10 C 4 x 5 C 1 (we choose 4 women from 10, and 1 man from 5)

Number of ways with at least 2 men = 15 C 5 - 10 C 5 - 10 C 4 x 5 C 1

To find the probability divide this by 15 C 5