Thread: Counting - Discrete math

7 woman and 9 man are on the faculty in the math department in the school.

(1) How many ways are there to select a committee of five members of the department if at least one woman must be on the same committee ?

(2) how many ways are there to select a committee of five members of the department if at least one woman and at least one man must be on the committee .

Can some one please help me with this ?

You are considering a set which has elements, and has a partition in two subsets and which have and elements.

For 1), what you want to know is the number of 5-element subsets of that have at least one element in . That means the "first" element must be in , you have choices, then every subset with elements in union is a solution.
So there are possible committees.

2) can be done is a similar way.