Question

In how many ways can 3 men and 3 women be seated around a round table such that all men are always together ?

Answer 1

Consider three men as one and arrange in $3!$ ways. And there are $3$ women. So total number of people is $4$.
These people can seat in round table in $(4-1)!=3!$ ways.
Hence total number of ways $=3!\times 3!=6\times 6=36$