The number of triangles that are formed by choosing the vertices from a set of 12 points,
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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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 = 12C3 – 7C3 = 220 -35 = 185
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