Algebra> permutations comibinations...

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

naren nagarajan , 14 Years ago

Grade Upto college level

3 Answers

Neer Varshney

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.

Last Activity: 14 Years ago

iit jee

hi,

no of quadrilaterals formed are 12C4-5C4

Last Activity: 14 Years ago

garima sharma

¹²c₄-⁵c₄-⁵c₃⁷c₁ (there ¹²c_{4 ways to select any number of quadrilaterals, we have to subtract}⁵c_{4 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}⁵c₃⁷c_{1 because this is the number of ways in which 3 collinear points will be selected and hence quadrilateral won't be formed})

Last Activity: 8 Years ago