Hello, Fox2013!

Seven women and nine men are on the faculty.

How many ways are there to select a committee of five people

(a) if at least one woman must be on the committee?

The opposite of "at least one woman" is "no women" (all men).

Therefore, there are: .

(b) if at least one woman and one man must be on the committee?

We musthave all-male committees nor all-female committees.not

In part (a), we found that are all-male committees.

Therefore, there are: .

. .