Question

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

Answer 1

Answer: (B)

We first select $2$ men out of $7$ in ${}^7{C}_2$ ways. Now we exclude the wives of these two selected men and so select $2$ ladies from remaining $5$ ladies in ${}^5{C}_2$ ways. Let $A,B$ be two men and $X,Y$ be the ladies playing in one set. Then we can have
(i) $A$ and $X$ plying against $B$ and $Y$.
(ii) $A$ and $Y$ playing against $B$ and $X$.
Then the total number of ways is ${}^7{C}_2\times {}^5{C}_2\times 2=21\times 10\times 2=420$.