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

Options

A. 756
B. 1512
C. 3024
D. none of these

Explanation

Out of 9 men two men can be chosen in `""^(9)C_(2)` ways. Since no husband and wife are to play in the same game, so, we have to select two women from the remaining 7 women. This can be done in `""^(7)C_(2)` ways. If `M_(1),M_(2)andW_(1),W_(2)` are chosen, then a team can be constituted in 4 ways viz. `M_(1)W_(2),M_(1)W_(1),M_(2)W_(1),M_(2)W_(2)`. Thus, the number of ways of arranging the game `=""^(9)C_(2)xx""^(7)C_(2)xx4=3024`.