Question

Six married couple are siting in a room. Number of ways in which $4$ people can be selected so that there is exactly one married couple among the four is

• A. $240$
• B. $255$
• C. $360$
• D. $480$

Answer 1

The correct option is A $240$

Out of $12$ people number of ways in which $12$ can be selected $={{}^{12}C}_4$

Now out of 4 let us find how many ways are there to selected exactly one married couple.

$\because$ there are $6$ married couple so $6$ ways.

After selecting couple, we select $1$ person from remaining $10$.

$9$ person remain from whom we have $8$ options.

So, no of ways $=\frac{10\times 8}{2!}$

$=40$

$\therefore$ Total ways $40\times 6=240.$

Hence, the answer is $240.$