There are n straight lines in a plane, no two are parallel and no three are concurrent. If the points of intersection of these lines are joined, then the number of new lines is

The n lines intersect in (n2) points. The number of lines formed by joining these points is 12(n2)((n2)−1) =12.n(n−1)2.(n(n−1)2−1)=18n(n−1)(n+1)(n−2) On each line there are n−1 pointsThe number of lines formed by these points is n(n−12)=n2(n−1)(n−2) The number of new lines is 18n(n−1)(n+1)(n−2)−n2(n−1)(n−2) =18n(n−1)(n−2)(n−3)=3(n4)