How many Triangles are formed in an octagon?

Answer 1

In a convex octagon, you can form triangles by selecting any three vertices. Since an octagon has 8 vertices, the number of ways to choose 3 vertices from these 8 is calculated using the combination formula ( \binom{n}{r} ), where ( n ) is the total number of vertices and ( r ) is the number of vertices to choose. Thus, the number of triangles formed is ( \binom{8}{3} = \frac{8!}{3!(8-3)!} = 56 ). Therefore, 56 triangles can be formed in an octagon.