Question

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

• A. $16$
• B. $28$
• C. $56$
• D. $70$

Answer 1

The correct option is A $16$

Required number of triangles $=$ total number of triangles$-$ number of triangles having two sides common $-$ number of triangles having one side common
$={}^8{C}_3-8-8\times 4=16$