In how many ways can friends sit at a circular table if two of them, Anna and Bob, insist on having exactly two people seated between them? (As usual, two seatings are considered the same if one is a rotation of the other.)
We can think of Anna and Bob as a single unit, so there are 8 units that need to be arranged around the table. This can be done in 7! ways. However, we need to divide by 2 since rotations of the arrangement are the same. So, the number of ways to arrange 9 friends around a circular table if two of them insist on having exactly two people seated between them is 7!/2 = 2520.