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 M

_{1}, M_{2}, W_{1}and W_{2}, the set of pairs may be
{(M

_{1},W_{1}) and (M_{2},W_{2})} Or
{(M

_{1},W_{2}) and (M_{2},W_{1})} ----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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