Saturday, 22 October 2011

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)

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