question_answer

The straight lines \[{{\ell }_{1}},{{\ell }_{2}},{{\ell }_{3}}\] and parallel and lie in the same plane. A total number of m points are taken on \[{{\ell }_{1}}\], n points on \[{{\ell }_{2}}\]. k points on \[{{\ell }_{3}}\]. The maximum number of triangles formed with vertices at these points are:

A) \[^{m+n+k}{{C}_{3}}\]

B) \[^{m+n+k}{{C}_{3}}{{-}^{m}}{{C}_{3}}{{-}^{n}}{{C}_{3}}{{-}^{k}}{{C}_{3}}\]

C) \[^{m}{{C}_{3}}{{+}^{m}}{{C}_{3}}{{+}^{k}}{{C}_{3}}\]

D) None of these