Five men and five women have to sit around a circular table so that no 2 women are together. In how many ways can that be done?  Choose the correct answer
A) 4!*5!	B) 6!*6!	C) 5!*7!	D) 6!*7!	E) 7!*7!
The number of arrangements of n distinct objects in a row is given by n!.   The number of arrangements of n distinct objects in a circle is given by (n-1)!.   The difference between placement in a row and that in a circle is following: if we shift all object by one position, we will get different arrangement in a row but the same relative arrangement in a circle. So, for the number of circular arrangements of n objects we have: n!/n=(n-1)!   Now, 5 men in a circle can be arranged in (5-1)! ways and if we place 5 women in empty slots between them then no two women will be together. The # of arrangement of these 5 women will be 5! and not 4! because if we shift them by one position we'll get different arrangement because of the neighboring men.   So the answer is indeed 4!*5!.   4!*5!
<result>A</result>
Five men and five women have to sit around a circular table so that no 2 women are together. In how many ways can that be done?