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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
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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