MathNet 1963 — Part 01 Question 4

It is considered a convex polygon of $n$ sides. All their diagonal lines are drawn and it is assumed that in no case do three of them concur at a point that is not a vertex, and that there are also no diagonals that are parallel. Under these conditions, you want to calculate:
a) The total number of intersection points of these diagonals, excluding vertices.
b) How many of these points are inside the polygon, and how many exteriors.