In a convex polygon with $n$ sides, what is the number of intersection points of the diagonals inside the polygon, given that no three of them are concurrent?
We call $A_{1}, \cdots, A_{n}$ the vertices, numbered in trigonometric order. For every set $A_{i}, A_{j}, A_{k}, A_{l}$, where $i<j<k<l$, there corresponds exactly one point $\mathrm{M}$:

![](https://cdn.mathpix.com/cropped/2024_05_10_8c44cd8b5c585c15e58bg-146.jpg?height=386&width=439&top_left_y=2100&top_left_x=797)

There are therefore $\binom{n}{4}$. 

## TD