The sides AB, BC & CA of a triangle ABC have 3, 4 and 5 interior points respectively on them.The number of triangles that can be constructed using these interior points as vertices will be?

we have following cases in this question:-
case (i): if one point is selected from each side then number of triangle is = 3×4×5 = 60
case (ii):  if one point is selected from one side and 2 points from another side then number of ways is
= ³C₂×(4 + 5) + ⁴C₂×(5+3) + ⁵C₂×(3+4)
= 3×9 + 6×8 + 10×7
= 27 + 48 + 70
= 145
So total number of triangle is 
= 60 + 145
= 205 Answer