Mathematics · Permutations and Combinations
Let ABC be a triangle. Consider 4 points p1, p2, p3, p4 on the side AB, 5 points p5, p6, p7, p8, p9 on the side BC, and 4 points p10, p11, p12, p13 on the side AC. None of these points is a vertex of the triangle ABC. Find the total number of pentagons that can be formed by taking vertices from the points p1, p2, ..., p13.
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