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10 points line in a plane of which 4 are collinear except these 4 points no three of the 10 points are collinear. How many distinct quadrilaterals can be drawn?
Dear Sohan if 4 points are collinear, from remaining 6 points there are 6C4 = 15 ways of choosing 4 vertices.there are 15 quadrilaterals , which can be formed from 6 such points.then 1 vertex from 4 collinear point and 3 vertices of quadrilateral from 6 points can be chosen in4C1 * 6C3 = 80now taking 2 vertices from 4 collinear points and 2 vertices from 6 points, this can be done in4C2 * 6C2 = 90 thus total number of quadrilaterals which can be formed from given points= 15+80+90= 185 RegardsArun (askIITians forum expert)
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