There are 10 points in a plane, out of these 6 are collinear. The number of triangles formed by joining these points, is

Solution:

A triangle is obtained by joining three noncollinear points. So number of triangles on joining 3 points out of 10 points =${ }^{10}{C}_3$.

But, 6 points are collinear and on joining any three out of these 6, we do not obtain a triangle .

Hence, the required number of triangles

${=}^{10}{C}_3{-}^6{C}_3=120-20=100$.