Question

The number of triangles which can be formed by using the vertices of a regular polygon of $(n+3)$ sides is $220$. Then, $n$ is equal to

• A. $8$
• B. $9$
• C. $10$
• D. $11$

Answer 1

The correct option is B $9$

Number of triangle $={}^{n+3}{C}_3=220$

$\therefore \frac{(n+3)!}{3!n!}=220$

$(n+1)(n+2)(n+3)=1320=12\times 10\times 11$

$=(9+1)(9+2)(9+3)$

$n=9$