Question

Number of ways in which a lawn tennis mixed double match be made from seven married couples if no husband and wife play in the same match is

• A. $240$
• B. $420$
• C. $720$
• D. $210$

Answer 1

The correct option is B $420$

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 $X$ playing against $B$ and $Y$

(ii) $A$ and $Y$ playing against $B$ and $X$

Then the total number of ways is ${}^7{C}_2{\times }^5{C}_2\times 2=21\times 10\times 2=420$.