In a plane,there are 10 points,out of which 4 | vedclass

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(B) To form a triangle,we need to select $3$ non-collinear points from the given set of points.Total number of ways to select $3$ points out of $10$ i

Vedclass · Accepted Answer

$116$

Vedclass · Answer

(B) To form a triangle,we need to select $3$ non-collinear points from the given set of points.Total number of ways to select $3$ points out of $10$ is given by $^{10}C_3$.$^{10}C_3 = \frac{10 	imes 9 	imes 8}{3 	imes 2 	imes 1} = 120$.Since $4$ points are collinear,any selection of $3$ points from these $4$ points will result in a straight line instead of a triangle.The number of ways to select $3$ points from these $4$ collinear points is $^4C_3$.$^4C_3 = \frac{4 	imes 3 	imes 2}{3 	imes 2 	imes 1} = 4$.Therefore,the number of triangles that can be formed is the total number of selections minus the selections that form a straight line:Number of triangles $= 120 - 4 = 116$.

In a plane,there are $10$ points,out of which $4$ are collinear. The number of triangles that can be formed by joining these points is:

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