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









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Option(B) is correct

As per the question there are 9 married couples and no husband and wife should play in the same game:

We know that in a mixed double match there are two males and two females.

Step I: Two male members can be selected in ${^9C_2} = 36$ ways

Step II: Having selected two male members, 2 female members can be selected in ${^7C_2} = 21$ ways.

Step III: Two male and two female members can arranged in a particular game in 2 ways.

Total number of arrangements,

$ = 36×21×2$

$= \textbf{1512 ways.}$

(2) Comment(s)

Shivam Chauhan

in the question it is mentioned 9 married couples , that means total 18 people , so first we select 2 men out of 9 and then again we select 2 women out of 9 because 9 couples means 9 male and 9 female , then they can be arranged in 2 ways i.e 36*36*2 =2592 ways


Other solution :

9P4 / 2 = 3024 / 2 = 1512 ways