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how many quadrilaterals can be formed from a set of 12 points in a plane.....of which 5 are collinear & no set of three points from remaining points lie on the same line

how many quadrilaterals can be formed from a set of 12 points in a plane.....of which 5 are collinear & no set of three points from remaining points lie on the same line

Grade:Upto college level

3 Answers

Neer Varshney
76 Points
11 years ago

Since 5 points are collinear so they can not form any other geometry else than straight line. So they can not form a quadrilateral.

And total number of quadrilaterals possible with 12 points are 12C4. And By 5 collinear points 5C4 quad. can be formed. 

So total number of quadrilaterals possible are 12C4 - 5C4.

iit jee
44 Points
11 years ago

hi,

no of quadrilaterals formed are 12C4-5C4

garima sharma
11 Points
5 years ago
12c4-5c4-5c37c1    (there 12c4 ways to select any number of quadrilaterals, we have to subtract 5c4 because this is the number ways in which 4 collinear points can be selected and hence won't form a quadrilateral adn we have to subtract 5c37c1 because this is the number of ways in which 3 collinear points will be selected and hence quadrilateral won't be formed)
 

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