Question

A committee of three people is to be chosen from four married couples. What is the number of different committees that can be chosen if two people who are married to each other cannot both serve on the committee?

Answer 1

Answer: 32

Explanation:

Since three (3) people are to be chosen from four (4) married couples without having two(2) married people in the same committee , it means each couple can only send one representative to the committee.

We can represent the couple using this illustration

MALE FEMALE

1. 1

2 2

3. 3

4. 4

For the first member of the committee, there are eight (8) possible choices.

(Assume we pick Female 1)

For the second member of the committee, there are six (6) possible choices. This is because we already picked Female 1and cannot pick Male 1. Let’s assume this time, we pick Male 2.

For the third member of the committee, we are left with four (4) choices. Don’t forget we already picked Female 1 and Male 2. That means we cannot pick Male 1 and Female 2.

The committee can be arranged in 3! Ways

3! = 3 × 2 × 1

= 6 ways

The different ways of selecting committee members can be gotten by multiplying the possible outcome for the first, second and third member and then divide by the ways the committee can be arranged (6)

1st member × 2nd member × 3rd member/ 6

= 32