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Wot n' Degeneration

Source: 2017 AIME I #1

March 8, 2017
2017 AIME I

Problem Statement

Fifteen distinct points are designated on △ABC\triangle ABC: the 3 vertices AA, BB, and CC; 33 other points on side AB‾\overline{AB}; 44 other points on side BC‾\overline{BC}; and 55 other points on side CA‾\overline{CA}. Find the number of triangles with positive area whose vertices are among these 1515 points.
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