- #1

elementbrdr

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## Homework Statement

If a polygon has n>=4 sides, what is the probability, in terms of n, that a triangle made up of vertices of the polygon shares at least one side with the polygon.## Homework Equations

## The Attempt at a Solution

Treating vertices of polygons as possible outcomes from which 3 are chosen: Sample space S =_{n}C

_{3}. I can't figure out how to express the number of outcomes within event E={number of triangles sharing at least one side with polygon}. My way of thinking about it is that values in E will be all combinations that contain at least a pair of consecutive numbers (which, since they represent vertices of the polgon, constitute a side of both the polygon and the triangle). Unfortunately, I can't come up with a way to express this algebraically. It may not even be the right approach.

Thanks for any help/advice.