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  4. If the sides AB , BC and CA of a triangle ABC have 3,5 and 6 interior points respectively, then the total number of triangles that can be constructed using these points as vertices, is equal to :

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Q. If the sides $AB , BC$ and $CA$ of a triangle $ABC$ have 3,5 and 6 interior points respectively, then the total number of triangles that can be constructed using these points as vertices, is equal to :

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Solution:

image
Total Number of triangles formed
$={ }^{14} C _{3}-{ }^{3} C _{3}-{ }^{5} C _{3}-{ }^{6} C _{3}$
$=333$