Question

The number of ways in which a mixed double game can be arranged from amongst $9$ married couples if no husband and the wife play in the same game is

• A. $756$
• B. $1512$
• C. $3024$
• D. None of the above

Answer 1

Answer: (C)

$3024$

For mixed doubles, we have $2$ men and $2$ women.

$2$ men out of $9$ can be selected in ${}^9{C}_8$ ways

Out of $9$ women, $2$ will be there wife $30$ only $7$ are remaining for selecting $2$

Now out of them $2$ possible combinations can be made.

So, total number of ways $={}^9{C}_2\times {}^7{C}_2\times 2$

$=3024$

Hence the answer is $3024.$