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  4. The sides AB, BC, CA of triangle ABC have 3, 4 and 5 interior points respectively on them. Find the number of triangles that can be constructed using these points as vertices

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Q. The sides $ AB,\,\,BC,\,\,CA $ of triangle $ ABC $ have $ 3,\,\,\,4 $ and $ 5 $ interior points respectively on them. Find the number of triangles that can be constructed using these points as vertices

Jharkhand CECEJharkhand CECE 2009

Solution:

Required number of triangles,
$ {{=}^{12}}{{C}_{3}}{{-}^{3}}{{C}_{3}}{{-}^{4}}{{C}_{3}}{{-}^{5}}{{C}_{3}} $
$ =220-1-4-10 $ $ =205 $