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Consider a 20-sided convex polygon K, wi...

Consider a 20-sided convex polygon K, with vertices `A_(1), A_(2),…, A_(20)` in that order. Find the number of ways in which three sides of K can be chosen so that every pair among them has at least two sides of K between them (For example `(A_(1), A_(2), A_(4), A_(5), A_(11) A_(12))` is an admissible triple while `(A_(1)A_(2), A_(4)A_(5), A_(19)A_(20))` is not)

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