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

185

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175

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115

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105

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Solution

The correct option is A
185

Required number of ways = $^{12} C_{3} -^{7} C_{3}$

= 220 - 35 = 185

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There are 10 points in a plane no three of which are in the same straight line, excepting 4 points, which are collinear.

Find the probability that

(i) number of straight lines obtained from the pairs of these points.

(ii) number of triangles that can be formed with the vertices as these points.

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