I am not sure how to approach this question.
How many ways are there to seat n couples around a circular table such that no couple sits next to each other?
Since it's a part of inclusion-exclusion, I'm supposed to use that method. But I have no clue how to approach this. I know total number of people are 2n and that's about it. I've looked at other stack exchange questions on the same exact problem but none of them helped...
- So I looked at the Menage problem, but that's seriously confusing - it's worse than other Mathexchange answers. In the solution, it mentions $d_k = (2n/2n-k) * C(2n-k,k) $. I have no clue where this guy came from.