(Q). The sides AB, BC, CA of a triangle ABC have 4, 5 and 6 interior points respectively on them. Find the number of triangles that can be constructed using given interior points as vertices?
Solution:-
Total number of points = 4 + 5 + 6 = 15
if none of them are collinear then number of triangle is = ¹⁵C₃
Reduce from this the number of triangle which will not be made due to collinear points but are being counted in ¹⁵C₃
Hence final number of triangle
= ¹⁵C₃ – ⁴C₃ – ⁵C₃ – ⁶C₃ Answer
