$p$ points are chosen on each of the three co planar lines. The maximum number of triangles formed with vertices at these points is :

Question

\[\begin {array} {1 1} (1)\;p^3+3p^2 & \quad (2)\;\frac{1}{2}(p^3+p) \\ (3)\;\frac{p^2}{2}(5p-3) & \quad (4)\;p^2(4p-3) \end {array}\]