(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known dataIf 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.

2. Relevant equations

3. The attempt at a solutionTreating 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.

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# Homework Help: Algebraic expression for triangles within polygons

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