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

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

A
$^{3 p} C_{3}$
B
$p^{2} (p - 1)$
C
$p^{2} (4 p - 1)$
D
$p^{2} (4 p - 3)$

Solution:

$p_{C_{1}} \times p_{C_{1}} \times p_{C_{1}} + p_{C_{2}} \times 2 p_{C_{1}} \times 3_{C_{1}} = p^{2} (4 p - 3)$

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