Question

Find the number of triangles formed by joining 12 points if no three points are collinear,

Answer 1

There are 12 points in a plane.
When no three of them are collinear.
We need three non-collinear points to form a triangle.
∴ The number of triangles formed ¹²C₃

= `(12!)/((12 - 3)!3!)`

= `(12!)/((9!3!)`

= `(12xx11xx10xx9!)/(3xx2xx1xx9!)`

= 220