Question

In how many ways can a party of 4 men and 4 women be seated at a circular table so that no two women are adjacent?

Answer 1

The 4 men can be seated at the circular table such that there is a vacant seat between every pair of men.

The number of ways in which these 4 men can be seated at the circular table = $3!=6.$

Now, the 4 vacant seats may be occupied by 4 women in ${}^4{P}_4=4!=24$ ways.

$\therefore$ the required number of ways = $(6\times 24)=144.$