Intersections in polygons

Question

I'm having troubles solving the following problem which is about combinatorics: let $n$ be a natural number $\ge 3$, and a convex polygon with $n$ vertices.

Each vertices are supposed to connect each other in straight lines, so that three lines never intersect at the same point.

The problem is about finding the number of intersections inside the polygon with respect to $n$, the number of vertices.

Here is an example with $n = 6$

Thanks a lot in advance !!

Answer 1

Hint: From a point of intersection, you find four of the $n$ vertices by following the two lines in both directions.