Question

The sides ab, bc, ca of a triangle abc have 3,4 and 5 interior points respectively on them. the total number of triangles that can be constructed by using these points as vertices is

Answer 1

Gonna use an image for this .
Question of combination

Answer 2

Answer:

= 333

Step-by-step explanation:

Selection of 3 points from given 14 points can be made in

         ¹⁴C₃ = 364          ------------> (1)

But selection of 3 points from the points on one line cannot give any triangle. Such selection are

            ³C₃ + ⁵C₃ + ⁶C₃

          = 1 + 10 + 20 = 31  -------------> (2)

Hence, total number of triangles that can be formed = 364 - 31 = 333

Good luck !!