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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

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a
105
b
15
c
175
d
185

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detailed solution

Correct option is D

We know, a triangle will be formed by taking three points at a time..'.Required number of triangles =12C3−7C3                                                  =12×11×103×2×1−7×6×53×2=220−35=185


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