Puzzle-11 (P&C) (IIFT-2008)

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

(A)  1514

(B)  1512

(C)  3024

(D) None of the above

Solution:

It involves selection of 2 men and 2 women first and then arrangements in between the pairs.

To select 2 men from the given 9 men      ------ 9C2 ways

To select 2 women from the given 9 women excluding the two, who are wives of already selected 2 men              ------ 7C2 ways

After selecting M₁, M₂, W₁ and W₂, the set of pairs may be

{(M₁,W₁) and (M₂,W₂)} Or

{(M₁,W₂) and (M₂,W₁)}          ----2 possibilities

Hence the total number of arrangements = 9C2 * 7C2 * 2

= (9*8/2) * (7*6/2) * 2 = 1512

Answer (B)