Question

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

Answer 1

It is given that no two lines are parallel means all line are intersecting and no three lines are concurrent means three lines intersect at a point.
`therefore` Number of point of intersection `=""^(20)C_(2) = (20"!")/(2"!" 18"!") = (20 xx 19 xx 18"!")/(2 xx 1 xx 18"!")`
`= (20 xx 19)/(2) = 19 xx 10 = 190`