1. The number of ways in which a mixed double tennis game can be arranged amongst 9 married couples if no husband and wife play in the same game is:
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By: anil on 05 May 2019 02.40 am
There are 9 married couples. Therefore, there will be 9 men and 9 women.
First, let us select the 2 men.
2 men can be selected in 9C2 = 36 ways.
Now, the wives of these 2 men cannot be selected. Therefore, we have to select 2 women from the remaining 7 women.
2 women can be selected in 7C2 = 21 ways.
We have selected 2 men and 2 women. A team should consist of one man and one woman. Therefore, the 2 teams can be formed in 2 ways.
Therefore, the total number of ways in which the team can be selected is 36*21*2 = 1512.
Therefore, option B is the right answer.
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First, let us select the 2 men.
2 men can be selected in 9C2 = 36 ways.
Now, the wives of these 2 men cannot be selected. Therefore, we have to select 2 women from the remaining 7 women.
2 women can be selected in 7C2 = 21 ways.
We have selected 2 men and 2 women. A team should consist of one man and one woman. Therefore, the 2 teams can be formed in 2 ways.
Therefore, the total number of ways in which the team can be selected is 36*21*2 = 1512.
Therefore, option B is the right answer.