Question

There is a set of 36 distinct points on a plane with the following characteristics: * there is a subset a consisting of fourteen collinear points. * any subset of three or more collinear points from the 36 are a subset of a. how many distinct triangles with positive area can be formed with each of its vertices being one of the 36 points? (two triangles are said to be distinct if at least one of the vertices is different)

Answer 1

The given data indicates that 14 points are collinear and remaining 22 points are non collinear.

A triangle can be formed by taking 1 points from 14 and 2 points from 22 (or) 2 points from 14 and 1 points from 22 (or) 3 points from 22

⇒ 14C1×22C2+14C2×22C1+22C3= 6776