The number of triangles that are formed by choosing the vertices from a set of 12 points, seven of which lie on the same line is

(A) 105 

(B) 15 

(C) 175

(D) 185

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1 Answers

Answer is (D)

Number of ways of selecting 3 points from given 12 points = 12C3

But any three points selected from given seven collinear points does not form triangle.

Number of ways of selecting three points from seven collinear points = 7C3 Required number of triangles = 12C37C3 = 220 -35 = 185

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