The number of triangles whose vertices are at the vertices of an octagon but none of whose sides happen to come from the sides of th octagon, is

The number of triangles

=Total number of triangles

- No. of triangles having one side common. with the octagon 

- No.  of triangles having two sides common with the octagon

${=}^8{C}_3{-}^8{C}_1{\times }^4{C}_1-8=16$.