JEE Main · 2026 · 22 Jan 2026 · Shift 1 · Permutations and Combinations

Let ABC be a triangle. Consider four points ${\mathrm{p}}_1,{\mathrm{p}}_2$, ${\mathrm{p}}_3,{\mathrm{p}}_4$ on the side AB , five points ${\mathrm{p}}_5,{\mathrm{p}}_6,{\mathrm{p}}_7,{\mathrm{p}}_8,{\mathrm{p}}_9$ on the side BC and four points ${\mathrm{p}}_{10},{\mathrm{p}}_{11},{\mathrm{p}}_{12},{\mathrm{p}}_{13}$ on the side AC . None of these points is a vertex of the triangle ABC . Then the total number of pentagons, that can be formed by taking all the vertices from the points ${\mathrm{p}}_1,{\mathrm{p}}_2,\dots .{\mathrm{p}}_{13}$, is ____ .