Question

The number of ways lawn tennis mixed double can be made up from seven married couples if no husband and wife play in the same set is .

• A. $210$
• B. $420$
• C. $840$
• D. $Noneofthese$

Answer 1

The correct option is B $420$

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 $21\times 10=210$.

Now suppose $A$ chooses $C$ as a partner ($B$ will automatically $go$ to $D$) or $A$ chooses $D$ as a partner, ($B$ will automatically go to $C$).

Thus we have $2$ choices for the teams.

Required number of ways is $210\times 2=420$.