Q. 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
Explanation
(b)
Number of triangles$= {\ ^{n + 3}C}_{3} = 220$
$\Rightarrow \ \ \ \ \ \ \ \frac{(n + 3)!}{3!n!} = 220$
$\Rightarrow \ \ \ \ \ \ (n + 1)(n + 2)(n + 3) = 1320$
$= 12 \times 10 \times 11$
$= (9 + 1)(9 + 2)(9 + 3)$
$\therefore\ \ \ \ \ \ \ \ \ \ \ n = 9$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.