There are 16 points in a plane,no three of wh | vedclass

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(A) To form a triangle,we need to select $3$ non-collinear points out of the given $16$ points.Total number of ways to select $3$ points from $16$ is

Vedclass · Accepted Answer

$504$

Vedclass · Answer

(A) To form a triangle,we need to select $3$ non-collinear points out of the given $16$ points.Total number of ways to select $3$ points from $16$ is given by $^{16}C_3 = \frac{16 	imes 15 	imes 14}{3 	imes 2 	imes 1} = 16 	imes 5 	imes 7 = 560$.However,$8$ points are collinear,meaning any selection of $3$ points from these $8$ will not form a triangle.The number of ways to select $3$ points from these $8$ collinear points is $^{8}C_3 = \frac{8 	imes 7 	imes 6}{3 	imes 2 	imes 1} = 56$.Therefore,the number of triangles that can be formed is the total combinations minus the invalid combinations: $560 - 56 = 504$.

There are $16$ points in a plane,no three of which are in a straight line except $8$ which are all in a straight line. The number of triangles that can be formed by joining them equals

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