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Question

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

A
n(n1)
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B
n(n1)2
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C
n2(n1)
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D
n2(n1)2
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Solution

The correct option is C n2(n1)
n points are taken at one line and another n points are taken at other lines.
Total 2n points are there in the plane in which n points are in a line and another n point are also in a line.

Hence, number of triangles =2nC3nC3nC3
=2n(2n1)(2n2)62n(n1)(n2)6
=13n(n1)(3n)=n2(n1)

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