Consider the five points comprising of the vertices of a square and the intersection point of its diagonals

Consider the five points comprising of the vertices of a square and the intersection point of its diagonals. How many triangles can be formed using these points?

  1. 4
  2. 6
  3. 8
  4. 10

Answer

You can form a triangle out of any 3 points which are not collinear. Hence, 3 points out of 5 can be chosen in 5C3 = 10 ways.

But of these, the three points lying on the two diagonals will be collinear.

So 10 - 2 = 8 triangles can be formed.

The correct option is C.