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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
Two coplanar lines that are not parallel intersect each other in a point.
There are 20 straight lines, no two of them 'are parallel and no three of them are concurrent.
So, the number of points of intersection
= 20C2
= `(20!)/((20 - 2)!2!)`
= `(20!)/(18!2!)`
= `(20 xx 19xx18!)/(2xx1xx18!)`
= 190
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