# 004 Sample Final A, Problem 17

How many ways can a committee of four people can be selected from five married couples if no committee is to include both husband-and-wife pairs? (simplify your answer to a single number)

Foundations
What is the maximum number of people we can choose from each couple to serve on the committee?
So, we have ${\displaystyle 5 \choose 4}$ ways to pick a 4 people from each couple.
So, there are ${\displaystyle 2{5 \choose 4}=10}$ ways to select a committee of four people.