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Question

There are 'n' straight line in a plane, no two of which are parallel and no three pass through the same point. Their points of intersection are joined. Then the maximum number of fresh lines thus introduced is

A
112n(n1)2(n3)
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B
18n(n1)(n2)(n+1)
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C
18n(n1)(n2)(n3)
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D
18n(n+1)(n+2)(n3)
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Solution

The correct option is B 18n(n1)(n2)(n+1)

No. of total points of intersection =nl2

=n(n1)2.

No. of maximum lens = no. of ways of selection of 2 points out of n(n1)2 points.

=n(n1)2×[n(n1)21]2

=18[n2(n1)22n(n1)]

=18n(n1)[n2n2]

=n(n1)(n2)(n+1)8


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