Question

In how many ways can 5 gentlemen and 5 ladies sit together at a
round table, so that no two ladies may be together?

Answer 1

As no ladies sit together first we arrange the men which can be done in (5-1)! = 4! ways 
and the ladies can be arranged in 5! ways 
there fore total no of ways in which they can be arranged = 4!*5! ways