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Question

The number of ways in which a mixed double game can be arranged from amongst 5 married couples if no husband and wife play in the same game is


A

56

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B

60

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C

96

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D

None of these

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Solution

The correct option is B

60


Explanation for the correct answer:

To play a match of mixed doubles, 4 people are required. 2 men and 2 women

There are 5 married couples implying there are 5 men and 5 women

2 men can be selected from the 5 men in C25 ways....(i)

Now we have to select the 2 women in such a way that neither of the selected men's wives are playing the game

So we do not include the 2 wives of the selected men in the selection for the 2 women in the game.

Hence,2 women can be selected out of the remaining 3 women in C23...(ii)

Now consider that 2 men and 2 women are selected to play the mixed doubles match say M1,M2 and W1,W2

The teams out of these 4 people can be M1,W1 and M2,W2 or M1,W2 and M2,W1.

That is the team can be made in 2 ways....(iii)

Hence, total number of ways=C25×C23×2

=5!2!3!×3!2!1!×2

Total number of ways=60

Hence, option (B) is the correct answer


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