In how many ways, we can choose two teams of mixed double for a tennis tournament from four couples such that if any couple participates, then it is in the same team?

In how many ways, we can choose two teams of mixed double for a tennis

1.	In how many ways, we can choose two teams of mixed double for a tennis tournament from four couples such that if any couple participates, then it is in the same team?
Answer» Correct Answer - 42 Case I when no couple is chosen We can choosen in `.^(4)C_(2)=6` ways and hence two teams can be formed in `2xx6=12` ways. Case II when only one couple is chosen A couple can be chosen in `.^(4)C_(1)=4` ways and the other team can be chosen in `.^(3)C_(1)xx.^(2)C_(1)=6` ways. hence, two teams can be formed in `4xx6=24` ways. Case III when two couples are chosen. then team can be chosen in `.^(4)C_(2)=6` ways. hence, total ways=12+24+6=42.

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In how many ways, we can choose two teams of mixed double for a tennis tournament from four couples such that if any couple participates, then it is in the same team?

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