There are points in a plane. Out of these, are collinear. The number of triangles formed by joining these points is:

Explanation: 1. Determine total possible selections: If no three points were collinear, the total number of triangles formed by points would be: 2. Account for collinear points: Collinear points lie on the same straight line. Selecting any points from the collinear points will not form a triangle; it will only form a line segment. We must subtract these "failed" triangles from the total. 3. Apply the Formula: 4. Step-by-Step Calculation: Calculate : Calculate : Subtract the values: Final Answer: The number of triangles formed is 100 . The correct option is (a) .

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NIMCET 2009 — Mathematics PYQ

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