There are $n$ points in a plane no three of which are in the same line except $p$ points which are collinear. The number of triangles formed by joining them is ?

^{n} C_{3}

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^{n} C_{3} -^{p} C_{3}

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^{n - p} C_{3}

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^{n} C_{3} -^{p} C_{3} + 1

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Solution

The correct option is C $^{n} C_{3}$
From $n$ points we can make triangles $=_{3}^{n} C$
But it will contain triangle made from $p$ colinear points which doesn't exist so we have to subtract the number of triangles made from $p$ colinear points.
No. of triangle made from $p$ colinear points $=_{3}^{p} C$
therefore number of triangles $=_{3}^{n} C -_{3}^{p} C$

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There are n points in a plane no three of which are in the same line except p points which are collinear. The number of triangles formed by joining them is ?

There are $n$ points in a plane no three of which are in the same line except $p$ points which are collinear. The number of triangles formed by joining them is ?