A group of twelve people want to sit around a round table with twelve seats. We don't care who is facing what direction, so if two seating arrangements differ only by a rotation of the whole table, we don't count them as different.
a) How many different ways can the group seat themselves?
b) Suppose that the group consists of six men and six women. How many different ways can the group seat themselves, if we insist that each man sit between two women and each woman sit between two men?
c) Suppose that the group consists of six men and six women. How many different ways can the group seat themselves, if we insist that each person sit between a man and a woman?