I have a circle with N points on it, and I want to determine how many triangles can be formed using these points.
How can I do this?
Each set of $3$ of the $N$ points determines a triangle, and each triangle is determined in this way, so all you have to do is determine how many $3$-element subsets a set of $N$ things has. If you don’t already know this, you should read this article.
The number of triangles that can be formed given N non collinear points is n = N(N-1)(N-2) / 6