One and only one straight line can be drawn passing through two given points and we can draw only one triangle through non-collinear points. By integral coordinates (x,y) of a point we mean both x and y as integers .
The number of triangles whose vertices are the vertices of an octagon but none of whose sides happen to be come from the octagon is

Options

A. 24
B. 52
C. 48
D. 16

Explanation

The numbers of triangles.
= Total number of trinangles
- 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)xx""^(4)C_(1)-8=16`.