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# Permutation and Combination

There are 8 concyclic points such that no two lines joining two of these points are parallel and no three lines joining three of these points are concurrent. Find the number of point of intersections of these lines which lie inside the circle.

Note by Arijit Banerjee
3 years, 10 months ago

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Choose 4 points out of these 8 points.You can form 2 intersecting lines out of these 4 points.Hence for every 4 points you get a point of intersection.Hence the total number of points of intersection = $$\binom{8}{3}$$ · 3 years, 9 months ago