Say you have N white balls and N black balls. How many distinguishable ways can I arrange them in a circle? If I were to arrange them in a line, I think there are $(2N)!/4$.

For N=2, there are 2 ways to arrange them: BWBW and WWBB.

Fr N=3, I think there are 4 ways: WWWBBB, WBWBWB, WWBBWB, WWBWBB

Say you have N white balls and N black balls. How many distinguishable ways can I arrange them in a circle? I consider 2 arrangements to be distinguishable if no rotation or reflection can make them the same.

If I were to arrange them in a line, I think there are $(2N)!/4$.

For N=2, there are 2 ways to arrange them: BWBW and WWBB.

For N=3, I think there are 4 ways: WWWBBB, WBWBWB, WWBBWB, WWBWBB