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I have a circle with N points on it, and I want to determine how many triangles can be formed using these points.

How can I do this?

Thanks!

Andrew

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    The question is unclear. What's the relevance of the points being on a circle ? Please show an example figure and pinpoint the triangles that should be counted.2016-03-31

2 Answers 2

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Each set of $3$ of the $N$ points determines a triangle, and each triangle is determined in this way, so all you have to do is determine how many $3$-element subsets a set of $N$ things has. If you don’t already know this, you should read this article.

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The number of triangles that can be formed given N non collinear points is n = N(N-1)(N-2) / 6