Nine men and nine 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 choice from the following choices:
A) 5!*6!  B) 6!*6!  C) 5!*7!  D) 6!*7!  E) 8!*9!
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, 9 men in a circle can be arranged in (9-1)! ways and if we place 9 women in empty slots between them then no two women will be together. The # of arrangement of these 9 women will be 9! and not 8! because if we shift them by one position we'll get different arrangement because of the neighboring men.   So the answer is indeed 8!*9!.   8!*9!
<result>E</result>
Nine men and nine women have to sit around a circular table so that no 2 women are together. In how many ways can that be done?