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

(1) 24 

(2) 56 

(3) 16 

(4) 48

Answer 1

Correct option is (3) 16   

∵ no. of triangles having no side common with a n

sided polygon \( =\frac{{ }^{n} C_{1} \cdot{ }^{n-4} C_{2}}{3}\)

\(=\frac{{ }^{8} \mathrm{C}_{1} \cdot{ }^{4} \mathrm{C}_{2}}{3}=16\)