The number of triangles that can be formed by choosing the vertices from a set o

Question

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

Options:

A . 185

B . 175

C . 115

D . 105

Answer: Option A
:
A
Required number of ways =

^{12} C_{3} -^{7} C_{3}

= 220 - 35 = 185

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