Need a hint regarding this question... In how many ways can we select three vertices from a regular polygon having $2n+1$ sides ($n>0$) such that the resulting triangle contains the centre of the polygon?

Hint: Distribute the remaining $2n-2$ vertices to the $3$ gaps between the chosen vertices. Find the number of ways to distribute them such that each gap contains no more than $n-1$ vertices. (because if a gap contains $n$ or more vertices, the centre of the polygon would be outside the triangle.)
