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
Correct Answer: B
Solution :
[b] The straight line \[{{l}_{1}},{{l}_{2}},{{l}_{3}}\] are parallel and lie in the same plane. Total number of points \[=m+n+k\] Total no, of triangles formed with vertices \[{{=}^{m+n+k}}{{C}_{3}}\] By joining three given points on the same line we don?t obtain a triangle. Therefore, the max. Number of triangles \[{{=}^{m+n+k}}{{C}_{3}}{{-}^{m}}{{C}_{3}}{{-}^{n}}{{C}_{3}}{{-}^{k}}{{C}_{3}}\]You need to login to perform this action.
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