You have a circular table with $N$ seats.$K$ bellicose guests are going visit your house of-course you don't want them to sit beside each other.As the host, you want to find out how many ways there are to choose $K$ seats such that none of them is adjacent to each other.
I noticed that there is a solution other than $0$ if ($N \ge 2K $) but I am not sure how to approach for the rest.
EDIT: Only $K$ bellicose guests are visiting,no friendly guest are there the remaining $N-K$ seats will be vacant.
A possible mathematical translation of this problem: Choosing $K$ candidate points from a circle of $N$ indistinguishable points such that there are more than one vacant point between adjacent candidate points.