There are 'n' straight line in a plane, no two of which are parallel and no three pass through the same point. Their points of intersection are joined. Then the maximum number of fresh lines thus introduced is
No. of total points of intersection =nl2
=n(n–1)2.
No. of maximum lens = no. of ways of selection of 2 points out of n(n–1)2 points.
=n(n–1)2×[n(n–1)2–1]2
=18[n2(n–1)2–2n(n–1)]
=18n(n–1)[n2–n–2]
=n(n–1)(n–2)(n+1)8