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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?

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?

Grade:12th pass

1 Answers

Arun
25750 Points
6 years ago
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 in
4C1 * 6C3 = 80
now taking 2 vertices from 4 collinear points and 2 vertices from 6 points, this can be done in
4C2 * 6C2 = 90
 
thus total number of quadrilaterals which can be formed from given points
= 15+80+90
= 185
 
Regards
Arun (askIITians forum expert)

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