Question

There are 20 straight lines in a plane so that no two lines are parallel and no three lines are concurrent. Determine the number of points of intersection

Answer 1

There are 20 lines such that no two of them are parallel and no three of them are concurrent.

Since no two lines are parallel

∴ they intersect at a point

∴ Number of points of intersection if no two lines are parallel and no three lines are concurrent

= ²⁰C₂

= `(20!)/(2!18!)`

= `(20 xx 19 xx 18!)/(2 xx 1 xx 18!)`

= 190