Question

The number of ways in which a mixed double game can be arranged amongst 9 married couples if no husband and wife play in the same game is

• A. 756
• B. 1512
• C. 30 24
• D. None of these

Answer 1

Answer: (B)

1512

Answer 2

We can choose two men out of 9 in ⁹C₂ ways. Since no husband and wife are to play in the same game, two women out of the remaining 7 can be chosen in ⁷C₂ ways. If M₁, M₂, W₁ and W₂ are chosen, then a team may consist of M₁ and W₁ or M₁ and W₂. Thus the number of ways of arranging the game is (⁹C₂) (⁷C₂) (2) =$\frac{9 \times 8}{2} \times \frac{7 \times 6}{2} \times 2$= 1512