A class contains 9 men and 3 women. Find the number of ways a teacher can select a committee of 4 from the class where there is
at least one woman on the committee.
We can solve this problem by finding the total number of ways to select a committee of 4 from the class, and then subtracting the number of committees with no women.
The total number of ways to select a committee of 4 from 12 people is:
${12 \choose 4} = \frac{12!}{4!8!} = 495$
To count the number of committees with no women, we need to select 4 men from a group of 9:
${9 \choose 4} = \frac{9!}{4!5!} = 126$
So the number of committees with at least one woman is:
$495 - 126 = 369$
Therefore, there are 369 ways for the teacher to select a committee of 4 with at least one woman.