Q.

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

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a

3pC3

b

p2(p−1)

c

p2(4p−1)

d

p2(4p−3)

answer is D.

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Detailed Solution

pC1×pC1×pC1+pC2×2pC1×3C1=p2(4p−3)

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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