how many triangles can be formed by connecting points of an n sided shape and m points inside the shape(without intersecting with other lines)

Question

i came across this problem recently, it looked like this:

there is an x sided shape, whats the maximum number of z sided shapes you can form with y additional points in the shape(within the shape) by connecting the lines. conditions: there is no absolute answer for where the y points are, and the lines cannot intersect with each other.

i tried solving by just drawing but shortly after i came across 2022 sided shapes.....(STRESS)...............