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**1. The problem statement, all variables and given/known data**

Find a formula for the number of ways to seat r of n people around a circular table, where seatings are considered the same if every person has the same two neighbors without regard to which side these neighbors are sitting on.

**2. Relevant equations**

None

**3. The attempt at a solution**

I understand the more basic form of this question; in order to seat n people, we have [itex]\frac{n!}{n}[/itex], since there are n! ways to seat n people and we divide out the n repetitions.

From there, we see that the ways to seat r of n people is simply [itex]\frac{P(n, r)}{r}[/itex]. So that gives us the first part of the problem.

But i'm not really sure where to go from here. I'm thinking, in this specific problem, we shouldn't be dividing out the r people, since it's explicitly stated that the only seating arrangements that are considered the same are where the same person has the same two neighbors. So i'm thinking, I definitely have the numerator: P(n, r). And.. then I hit a wall.

Any help is appreciated.