Question

No of ways in which 4 men and 4 womn can be seated at round table so that no two women may be together

Answer 1

4 men can sit at 4 seats in: 
4P4 = 4! = 24 ways 

now consider one position between each two adjecent men. 4 women need to sit in these 4 spots in order for condition to be valid (no two men together). this can, again, be done in: 
4P4 = 24 ways.