Question

There are n points in a plane, no three being collinear except m of them which are collinear. The number of triangles that can be drawn with their vertices at three of the given points is

• A. ${}^{n-m}{C}_3$
• B. ${}^n{C}_3{-}^m{C}_3$
• C. ${}^n{C}_3-m$
• D. None of these

Answer 1

The correct option is B ${}^n{C}_3{-}^m{C}_3$

Given n points the number of triangles that can be drawn by joining any three non - collinear points ${}^n{C}_3$ out of this ${}^m{C}_3$ is to be subtracted as m points are collinear and no triangle is possible within the m points. Hence, Number of triangles = ${}^n{C}_3$ - ${}^m{C}_3$