I'm looking for a proof for this question/near-answer
Take any set of $K$ points on the plane where no $3$ are colinear. How many line segments can be created, regardless of order, before any intersect?
Create a convex polygon using the points as vertices, such that it encompasses all other points, it will be an $N$-gon. Then with the remaining interior points do the same, until you have no points, the last polygon(sometimes a line or point) will have $V$ vertices.
The number will be based on $K,N,\&V$ and will roughly be $3N-K$