Question

If $20$ lines are drawn in a plane such that no two of them are parallel and no three are concurrent, in how many points will they intersect each other?

Answer 1

Given : Out of $20$ lines, no two lines are parallel and no three lines are concurrent.

Number of point of intersection
$={}^{20}{C}_2=\frac{20!}{(20-2)!\times 2!}$

$(\because {}^n{C}_r=\frac{n!}{r!(n-r)!})$

$=190$

$\therefore$ Number of point of intersection $=190$