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

Q: 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) 2 . ⁹C₂⁷C₂

(D) none of these

Sol. 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) = 1512.

Hence (B), (C) are the correct answer.