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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
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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