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  • 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?

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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If no two lines are parallel, all lines are intersecting, and no three lines are concurrent.

Two straight lines create one point of intersection

Number of points of intersection = Number of combinations of 20 straight lines taken two at a time

=^{20}{C_{2}}=\frac{20 !}{2 ! 18 !}=20 * \frac{19}{2 * 1}=190

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infoexpert21

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