Question

How many triangles can be formed using 20 points no two points are collinear​

Answer 1

To form a triangle u need 3 random non collinear points

Now assume all are non collinear

So triangles formed will be

we can write 20! as 20*19*18*17! Cancel the 17! from both sides to get 20*19*18 / 6

I.e 1140

Now 6 points are collinear so minus 6C3 which is (6*5*4)/ (3*2) which is 20

So no of triangles formed actually will be 1140–20=1120

Now

I don't know why people have taken 15C3 . I think they have taken 20–6+1

Which is wrong as they are missing out points which are collinear and can form triangles with non collinear points.

Suppose there are n points in a plane out of which m points are collinear. Number of triangles that can be formed by joining these n points as vertices

= nC3 - mC3