Question

There are 3 men and 7 women taking a dance class. If $N$ is number of different ways in which each man be paired with a woman partner, and the four remaining women be paired into two pairs each of two, then the value of $\frac{N}{90}$ is

Answer 1

The required men and women pair can be made in ${}^7{P}_3$ ways
and from $4$ womens two groups can be made in $\frac{4!}{2!\cdot 2!\cdot 2!}$ ways
So total number of ways $N=210\times 3=630$
$\therefore \frac{N}{90}=7$