2017 AIME I Problem 1

Fifteen distinct points are designated on \triangle ABC: the 3 vertices A, B, and C; 3 other points on side \overline{AB}; 4 other points on side \overline{BC}; and 5 other points on side \overline{CA}. Find the number of triangles with positive area whose vertices are among these 15 points.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.