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

1. A

2. B

${\mathrm{p}}^{2}\left(\mathrm{p}-1\right)$

3. C

${\mathrm{p}}^{2}\left(4\mathrm{p}-1\right)$

4. D

${\mathrm{p}}^{2}\left(4\mathrm{p}-3\right)$

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${\mathrm{p}}_{{\mathrm{C}}_{1}}×{\mathrm{p}}_{{\mathrm{C}}_{1}}×{\mathrm{p}}_{{\mathrm{C}}_{1}}+{\mathrm{p}}_{{\mathrm{C}}_{2}}×2{\mathrm{p}}_{{\mathrm{C}}_{1}}×{3}_{{\mathrm{C}}_{1}}={\mathrm{p}}^{2}\left(4\mathrm{p}-3\right)$