• # question_answer ABCD is a convex quadrilateral. 3, 4, 5 and 6 points are marked on the sides AB, BC, CD and DA respectively. Find the number of triangles with vertices on different sides. A) 215 B) 342 C) 225 D) 424

 the number of triangles with vertices on sides $AB,BC,CD={}^{3}{{C}_{1}}\times {}^{4}{{C}_{1}}\times {}^{5}{{C}_{1}}$Similarly for other cases $\therefore$The total number of triangles $={}^{3}{{C}_{1}}\times {}^{4}{{C}_{1}}\times {}^{5}{{C}_{1}}\times {}^{3}{{C}_{1}}\times {}^{4}{{C}_{1}}\times {}^{6}{{C}_{1}}$$+{}^{3}{{C}_{1}}\times {}^{5}{{C}_{1}}\times {}^{6}{{C}_{1}}+{}^{4}{{C}_{1}}\times {}^{5}{{C}_{1}}\times {}^{6}{{C}_{1}}=342$