6 women and 5 men are to be seated in a row so that no 2 men can sit together. Number of ways they can be seated is
Condition is that no 2 men can sit together.
One of the ways to achieve this is to first make 6 women to sit together and arrange 5 men in the gaps as shown below.
6 women can be made to sit together in 6! ways.
Observe that there are 7 places and 5 men are to be seated in these 7 places.
In other words, for 5 men, we have to arrange 5 places from the available 7 places. This can be done in 7P5 ways
So, the total number of ways they can be seated = 6! ×7P5