The number of triangles whose vertices are at the vertices of a regular octagon but none of whose sides is a…
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
48
56
24
16
Solution
$\because$ no. of triangles having no side common with a $\mathrm{n}$
$\begin{aligned}
& \text { sided polygon }=\frac{{ }^n C_1 \cdot{ }^{n-4} C_2}{3} \\
& =\frac{{ }^8 C_1 \cdot{ }^4 C_2}{3}=16
\end{aligned}$