There are 11 points in a plane,of which 5 poi | vedclass

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(A) To form a quadrilateral,we need to select $4$ points out of $11$ such that no $3$ points are collinear. Total ways to select $4$ points from $11$

Vedclass · Accepted Answer

$265$

Vedclass · Answer

(A) To form a quadrilateral,we need to select $4$ points out of $11$ such that no $3$ points are collinear. Total ways to select $4$ points from $11$ is given by $^{11}C_4 = \frac{11 	imes 10 	imes 9 	imes 8}{4 	imes 3 	imes 2 	imes 1} = 330$. However,if we select $3$ or $4$ points from the $5$ collinear points,they will not form a quadrilateral. Ways to select $4$ points from $5$ collinear points is $^{5}C_4 = 5$. Ways to select $3$ points from $5$ collinear points and $1$ point from the remaining $6$ points is $^{5}C_3 	imes ^{6}C_1 = 10 	imes 6 = 60$. Total invalid selections = $5 + 60 = 65$. Number of quadrilaterals = $330 - 65 = 265$.

There are $11$ points in a plane,of which $5$ points are collinear. The total number of distinct quadrilaterals that can be formed with vertices at these points is:

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