Question

The straight lines $I_1,I_2,I_3$ are parallel and lie in the same plane. A total number of m points on $I_1$, n points on $I_2$, k points on $I_3$ are used to produce the triangles, the maximum number of triangles formed with vertices at these points are:

• A. ${}^m{C}_3{\times }^n{C}_3{\times }^k{C}_3$
  
• B. ${}^{(m+n+k)}{C}_3-{(}^m{C}_3{+}^n{C}_3{+}^k{C}_3)$
  
• C. ${}^{(m+n+k)}{C}_3$
  
• D. None of the above

Answer 1

The correct option is B ${}^{(m+n+k)}{C}_3-{(}^m{C}_3{+}^n{C}_3{+}^k{C}_3)$


Required number of triangles =${}^{m+n+k}{C}_3{-}^m{C}_3{-}^n{C}_3{-}^k{C}_3$