The number of triangles whose vertices are at the vertices of a regular octagon but none of whose sides is a side of the…
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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
[JEE Main 2024, 06 Apr (Shift 1)]
✓ Correct answer: c)
16
Explanation
\(∵\) No. of triangles having no side common with an sided polygon
\(=\frac{{}^{n}{C}_{1}{.}^{n−4}{C}_{2}}{3}\)
\(=\frac{{}^{8}{C}_{1}{.}^{4}{C}_{2}}{3}=16\)
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