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Question
If 20 lines are drawn in a plane such that no two of them are parallel and no three are concurrent, in how many points will they intersect each other?
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Solution
Given that out of 20 lines, no two lines are parallel and no three lines are concurrent.
Therefore, number of point of intersection
= 20C2 ......[∵ For any point of intersection, we need two lines]
= `(20*19)/(2*1)`
= 190
Hence, the required number of points = 190.
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