Say I wish to form exactly two non-intersecting triangles using vertices of an $n$ sided polygon.

How many ways would there be of doing this?

The condition is that the vertices **must be distinct**. In other words, we **cannot share vertices**.

I have below an example of a 'good' set of triangles.

[![enter image description here](https://i.stack.imgur.com/MxCnZ.jpg)](https://i.stack.imgur.com/MxCnZ.jpg)

I am not even sure where to begin here.