Question

If a team of 4 persons is to be selected out of 4 married couples to play mixed doubles tennis game, then the number of ways of forming a team in which no married couple appears is

• A. 12
• B. 8
• C. 6
• D. 24

Hint:

In problems avoiding couples or pairs, choose the group and exclude their corresponding partners from the next step.

Answer 1

The Correct Option is A

Each married couple contributes 1 man and 1 woman. So we have 4 men and 4 women.
We need to form a team of 2 men and 2 women such that no married couple appears.
Step 1: Choose 2 men from 4: \( \binom{4}{2} = 6 \) ways
Step 2: For each chosen pair of men, exclude their wives and choose 2 women from the remaining 2: \( \binom{2}{2} = 1 \) way
So total = \( 6 \times 1 = 6 \) But we can also choose 2 women first and exclude their husbands. So again we get 6 new combinations.
However, these are not double counted since pairings are distinct. So total = \( 6 + 6 = 12 \)