Question

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

Answer 1

Total number of points `12`. If no three points are co-linear thentotal number of triangles would be `""^12C_3` . But 3 points on AB ,4 points on BC and 5 points on CA are co-linear , So total number of triangles formed should be

`=""^12C_3-(""^3C_3+""^4C_3+""^5C_3)=220-(1+4+10)=205` .