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:

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

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

The straight lines \[{{\ell }_{1}},{{\ell }_{2}},{{\ell }_{3}}\] and p

1.	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
Answer» C. \[^{m}{{C}_{3}}{{+}^{m}}{{C}_{3}}{{+}^{k}}{{C}_{3}}\]

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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:

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