Points on a Plane 1
Fifteen points are drawn in the plane in a such way that besides which are collinear ,no other points are collinear.
Find the number of straight lines which pass through at least 2 of the 15 points.
The answer is 96.
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1 solution
Each of the lines is determined by a pair of points. In total we can choose ( 2 1 5 ) pairs of points. However all the pairs made up of P 1 , P 2 , P 3 , P 4 , P 5 , which are collinear actually determine just one line, so we have to subtract those and instead just add one. The solution is ( 2 1 5 ) − ( 2 5 ) + 1 = 9 6