How many ways can a committee of four people can be selected from five married couples if no committee is to include both husbandandwife 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?

Answer:

We can at most choose one person from each couple to serve on the committee.

Solution:
Step 1:

We can at most choose 1 person from the husband and wife pairs.

So, we have $5 \choose 4$ ways to pick a 4 people from each couple.

Step 2:

But, then for each couple, we could choose the husband or the wife to serve on the committee.

So, there are $2{5 \choose 4}=10$ ways to select a committee of four people.

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