Eleven men and eleven 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 answers:
A) 5!*6!
B) 7!*8!
C) 10!*11!
D) 10!*12!
E) 11!*12!
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, 11 men in a circle can be arranged in (11-1)! ways and if we place 11 women in empty slots between them then no two women will be together. The # of arrangement of these 11 women will be 11! and not 10! because if we shift them by one position we'll get different arrangement because of the neighboring men.   So the answer is indeed 10!*11!.   10!*11!
<result>C</result>
Eleven men and eleven women have to sit around a circular table so that no 2 women are together. In how many ways can that be done?