# How many closed polygons $n$ lines make on a plane?(not duplicate) [duplicate]

This question already has an answer here:

How many closed polygons will $n$ coplanar lines, all intersecting each other (no three concurrent), form on the plane?

Can we find a recursion formula for this?? Is there a way out?

## marked as duplicate by Parcly Taxel, Community♦Mar 2 '18 at 3:57

• Is it $\frac{n^2-3n+2}{2}$ ?? – Of course it's not me Mar 2 '18 at 4:02