Question

Find the number of triangles formed whose vertices are also a vertices of regular octagon but the side of triangle is not common with sides of octagon is___

Answer 1

Correct answer is : 56

⇒ Total triangles = ⁸C₃ 

Triangles with all 3 sides common with octagon = 0 

Triangle with 2 sides common with octagon ⇒ Choose vertex

= (⁸C₁) ⇒ 8 triangles

Triangle with exactly 1 side common

= (⁸C₁) ways to choose a side, remaining vertex can be selected in 4 vertices = ⁴C₁ ways = ⁸C₁.⁴C₁ = 32

⇒ 56 – (8 + 0 + 32) = 16 triangles