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Q.

Two straight lines intersect at a point O. Points A1, A2, …, An are taken on one line and points B1, B2, …, Bn on the other. If the point O is not to be used, the number of triangles that can be drawn using these points as vertices, is

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a

n (n – 1)

b

n (n – 1)2

c

n2 (n – 1)

d

n2 (n – 1)2

answer is C.

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Detailed Solution

No. of triangles =nC1.nC2+ nC1.nC2=2n.n(n−1)2=n2(n−1)
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Two straight lines intersect at a point O. Points A1, A2, …, An are taken on one line and points B1, B2, …, Bn on the other. If the point O is not to be used, the number of triangles that can be drawn using these points as vertices, is