Single Choice

The number of triangles whose vertices are at the vertices of an octagon but none of whose sides happen to come from the sides of the octagon is

A$$24$$
B$$52$$
C$$48$$
D$$16$$
Correct Answer

Solution

Total number of triangles formed will be $${ ^{ 8 }{ C } }_{ 3 }=56$$

Number of triangles formed with two side common with octagon is $$8$$

Number of triangles formed with only one side common with octagon is $$8 \times 4=32$$

Therefore the number of triangles whose vertices are at the vertices of an octagon but none of whose sides happen to come from the side of octagon is $$56-8-32=16$$

SIMILAR QUESTIONS

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Given a line I and a point P on it. How many lines can be drawn passing through the point P?

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