Combinatorics, Circular Permutations

Circular Permutations

How many ways can n people sit at a round table? These are circular permutations.

If one of the chairs is designated as the "head" of the table, then the answer is n!. Any of n people sits at the head of the table, and the permutation proceeds in a clockwise direction.

Now, since the chairs are indistinguishable, it doesn't matter who sits at the head, so divide by n, giving (n-1)!.

Once one chair is chosen as the head, there are n! arrangements