Permutation and Combination

Question

In how many different ways can 5 girls and 5 boys form a circle such that the boys and the girls alternate?
Why the answer is 4! * 5! rather than 5!*5!.
I know that for circular arrangement it is (n-1)! But why ?

Answer 1

Actually, number of ways of arranging a $n$ distinct objects in a row would be $n!$. Now think that we shift each person one place back, and bring the last person in front. This will give a new linear arrangement, but if the starting point and end point are joined, this arrangement will be same as old one! There will be $n$ such redundant countings, so we divide $n!$ by $n$.