Question

How many triangles can be formed by joining the vertices of an octagon?

• A. $56$
• B. $28$
• C. $112$
• D. $120$

Answer 1

Answer: (A)

$56$

Octagon : $8$ sided polygon

No three points are collinear

For a triangle three points are needed selecting three points of eight

${}^n{C}_r=\frac{n!}{(n-r)!r!}{}^{}{}^8{C}_3\Rightarrow \frac{8!}{5!\times 3!}\Rightarrow \frac{8\times 7\times 6}{3\times 2}\Rightarrow 56$

Therefore $56$ Triangles are possible