There are three coplanar parallel lines. lf any p points are taken on each of the lines, the maximum number of triangles with vertices on these points is

Select any three points from total 3p points, which can be done  3pC3 ways. But this also includes selection of three collinear points. Now three collinear points from each straight line can be selected in  pC3 ways. Then the number of triangles is  3pC3−3pC3=p2(4p−3).