Permutations & Combinations
Triangles in Regular Octagon — No Side of Octagon
nta_pyq_2024_apr
Grade 11
Question:
The number of triangles whose vertices are at the vertices of a regular octagon but none of whose sides is a side of the octagon is
Step-by-Step Solution
Key Concept: For a regular $n$-gon, triangles with no side being a side of the polygon: $\frac{n\cdot^{n-4}C_2}{3}$. For $n=8$: $\frac{8\cdot^4C_2}{3}=\frac{8\cdot6}{3}=16$.
$\frac{8\cdot^4C_2}{3}=16$.
Correct Answer: 4