How many triangles can be drawn by using 9 no | vedclass

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(A) To form a triangle,we need to select $3$ non-collinear points out of the given points.Since all $9$ points are non-collinear,any selection of $3$

Vedclass · Accepted Answer

$84$

Vedclass · Answer

(A) To form a triangle,we need to select $3$ non-collinear points out of the given points.Since all $9$ points are non-collinear,any selection of $3$ points will form a unique triangle.The number of ways to select $3$ points from $9$ is given by the combination formula $^nC_r = \frac{n!}{r!(n-r)!}$.Here,$n = 9$ and $r = 3$.Therefore,the number of triangles = $^9C_3 = \frac{9 	imes 8 	imes 7}{3 	imes 2 	imes 1} = 3 	imes 4 	imes 7 = 84$.

How many triangles can be drawn by using $9$ non-collinear points?

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