In how many ways can a mixed doubles game in tennis be arranged from 5 married couples, if no husband and wife play in the same game?

Answer

60

Explanation

Now, let sides of game be A and B. given 5 married couples i.e., 5 husbands and 5 wives. Now 2 husbands for two sides A and B be selected out of `5=.^(5)C_(2)=10` ways.
After choosing the two husbands their wives are to be excluded (since no husband and wife play in the same game). so, we are to choose 2 wives out of remaining 5-2=3 wives i.e., `.^(3)C_(2)=3` ways. again two wives can interchange their sides A and B in 2@=2 ways.
by the principle of multiplication.
The required number of ways`=10xx3xx2=60`.