## 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)!.