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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?
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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