how many triangles are determined by 12 points in a plane, If the points are used as vertices and if 7 of the points lie in the same straight line

Question

It is the question of combination

Answer 1

Let's assume that none of the triangles share any vertices, then 12 points would make 4 triangles.

It takes two points to form a base, so 6 points would form the bases of 3 triangles, and these bases lie on the same line, so we would need a 4th point in line with the other. This could be the vertex of the 4th triangle.

For example:

The 7 collinear points are A, B, D, E, G, H, L, The remaining points (vertices) C, F, I, J, K are not collinear.