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1. 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:
We know that in a mixed double match there are two males and two females.
Step I: Two male members can be selected in 9C2 = 36 ways.
Step II: Having selected two male members, 2 female members can be selected in,
7C2 = 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
= 1512 ways
Solution:
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 9C2 = 36 ways.
Step II: Having selected two male members, 2 female members can be selected in,
7C2 = 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
= 1512 ways