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

42

Explanation

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.