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Question
There are 20 straight lines in a plane so that no two lines are parallel and no three lines are concurrent. Determine the number of points of intersection
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Solution
There are 20 lines such that no two of them are parallel and no three of them are concurrent.
Since no two lines are parallel
∴ they intersect at a point
∴ Number of points of intersection if no two lines are parallel and no three lines are concurrent
= 20C2
= `(20!)/(2!18!)`
= `(20 xx 19 xx 18!)/(2 xx 1 xx 18!)`
= 190
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