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The Mid-Point Theorem

If the sides ...

Question

If the sides $A B, B C$ and $C A$ of a triangle $A B C$ 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:

A

360

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B

240

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C

333

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D

364

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Solution

The correct option is C $333$
Total number of triangles $=^{(3 + 5 + 6)} C_{3} -^{3} C_{3} -^{5} C_{3} -^{6} C_{3}$
$= 364 - 1 - 10 - 20 = 333$

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