Number of ways in which a lawn-tennis mixed double be made from seven married couples if no husband and wife play in the same set is a. `240` b. `420` c. `720` d. none of these

Explanation

Let the two husbands A, B be selected out of seven males in `7_(C_2)​ = 21` ways.

Excluding their wives we have to select two ladies C, D out of remaining 5 wives in `5_(C_2)​ = 10` ways.

Thus the number of ways of selecting the players for mixed double is `21 xx 10 = 210`

Now suppose A chooses C as a partner or A chooses D as a partner,

Thus we have 2 choices for the teams.

Required number of ways is `210 xx 2 = 420`.