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Equal Angles Subtend Equal Sides

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Question

There are $14$ points in a plane out of which $4$ are collinear. Find the number of triangles formed by the points as vertices.

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Solution

triangle is formed by Joining 3 pt.t
& '4' collinear pt . can't from triangle
$\Rightarrow$ no.of ways $=^{14} C_{3} -^{4} C_{3} = 360$

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