A committee of 3 is chosen at random from 4 men and 3 women. What is the probability that it has at least one woman?

Explanation

1. 01

   Use the complement: no woman means all 3 are men, in ${}^{4}C_3 = 4$ of the ${}^{7}C_3 = 35$ ways.

2. 02

   So the probability is $1 - \frac{4}{35} = \frac{31}{35}$.