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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?

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?

Grade:

4 Answers

Askiitians Expert Sahil Arora - IITD
19 Points
11 years ago

Dear  s adhithya

In mixed doubles, there are 2 men and 2 women..

2 men out of 9 can be selected in 9cways.

now we can only set 2 women out of 7.bec two the selected two men's wife can't play in a match

so in 7cwe can select women

now there are 2 men and 2 women M1, M2, W1,W2

possible combinatoin:

M1W1  and M2W2

M1W2 and M2W1..

so 2 possible combination..

hence answer= 9c*  7c*2

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Regards,

Askiitians Experts

Sahil Arora
s adhithya s
4 Points
11 years ago

Dear Sir,

I still have a doubt after seeing your reply. The answer you have given is what i arrived at myself on encountering the question in my bitsat sample paper, 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 sit out. why aren't these 2 cases being considered?

Shardul
16 Points
2 years ago
Dear adhitya answer would be the same in both casesyou can just use 9c2 for men and women and apply PNC
Rishi Sharma
askIITians Faculty 646 Points
one year ago
Dear Student,
Please find below the solution to your problem.

In mixed doubles, there are 2 men and 2 women..
2 men out of 9 can be selected in9c2ways.
now we can only set 2 women out of 7.bec two the selected two men's wife can't play in a match
so in7c2we can select women
now there are 2 men and 2 women M1, M2, W1,W2
possible combinatoin:
M1W1 and M2W2
M1W2 and M2W1..
so 2 possible combination..
hence answer=9c2*7c2*2

Thanks and Regards

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