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The number of ways in which a mixed double game can be arranged from amongst 9 married couples if no husband and wife play in the same game is? I have gotten an answer for this question, but even after seeing it I still have a doubt. Could you please help? The answer I have been given is what i arrived at myself on first encountering the question, but on 2nd thoughts, i felt that besides the case of 2 men being chosen out of 9 and then 2 women being selected out of 7, there is also the possible case of 2 women being selected out of 9 and then 2 men being selected out of 7 and also the third case of 2 men being selected out of eight and then 2 women being selected out of 8 , i.e, a husband from 1 couple and a wife from another couple play the game. why aren't these 2 cases being considered?

The number of ways in which a mixed double game can be arranged from amongst 9 married couples if no husband and wife play in the same game is? I have gotten an answer for this question, but even after seeing it I still have a doubt. Could you please help? The answer I have been given is what i arrived at myself on first encountering the question, but on 2nd thoughts, i felt that besides the case of 2 men being chosen out of 9 and then 2 women being selected out of 7, there is also the possible case of 2 women being selected out of 9 and then  2 men being selected out of 7 and also the third case of 2 men being selected out of eight and then 2 women being selected out of 8 , i.e, a husband from 1 couple and a wife from another couple play the game. why aren't these 2 cases being considered?

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1 Answers

SHAIK AASIF AHAMED
askIITians Faculty 74 Points
6 years ago
Hello student,
Please find the answer to your question below
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 in9C2=36ways
Step II:Having selected two male members, 2 female members can be selected in7C2=21ways.
Step III:Two male and two female members can arranged in a particular game in 2 ways.
Total number of arrangements=36×21×2=1512ways.

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