Question

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

Answer 1

A triangle can be formed by selecting 3 non-collinear points.

We can choose 3 points from 12 points in

¹²C₃ = `(12!)/(3!9!)`

= `(12 xx 11 xx 10 xx 9!)/(3 xx 2 xx 1 xx 9!)`

= 220 ways

∴ number of triangles = 220.