Out of 10 points in a plane,6 are in a straig | vedclass

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(A) 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 from $10$ poi

Vedclass · Accepted Answer

$100$

Vedclass · Answer

(A) 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 from $10$ points is $^{10}C_3 = \frac{10 	imes 9 	imes 8}{3 	imes 2 	imes 1} = 120$.Since $6$ points are collinear,any selection of $3$ points from these $6$ points will not form a triangle.The number of ways to select $3$ points from these $6$ collinear points is $^6C_3 = \frac{6 	imes 5 	imes 4}{3 	imes 2 	imes 1} = 20$.Therefore,the number of triangles formed = $^{10}C_3 - ^6C_3 = 120 - 20 = 100$.

Out of $10$ points in a plane,$6$ are in a straight line. The number of triangles formed by joining these points is:

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