Question

Out of 18 points in a plane, no three are in the same straight line except five points, which are collinear. Find the number of

(a) straight lines 

(b) triangles which can be formed by joining them.

Answer 1

Out of 18 points, 5 are collinear.

(a) Number of straight lines

= ¹⁸C₂ - ⁵C₂ + 1 = 153 - 10 + 1 = 144

(b) Number of triangles

=  ¹⁸C₃  - ⁵C₃ = 816 - 10 = 806