Question

In a plane 8 points are colliner out of 12 points, then the number of triangles we get with those 12 points is
A) 20
B) 160
C) 164
D) 220

Answer 1

The answer will be
c)164

Answer 2

Answer:

For a triangle, we need 3 non-collinear points. So with 12 points (when all the 12 are such that any three non-collinear is12C₃. But among them 8 points are collinear.

If all these 8 points are different we get 8C₃ triangles as they are collinear.

In 12C₃ triangles, we do not get 8C₃ triangles

↠ The number of triangles we get = 12C₃ – 8C₃

= 164

∴ Correct Option will be C ) 164.