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:

360

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240

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364

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333

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Solution

The correct option is D $333$
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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If the sides AB,BC and CAof 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:

The correct option is D 333Total number of triangles =(3+5+6)C3−3C3−5C3−6C3 =364−1−10−20=333

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:

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