(Q). Let Tₙ be the number of all possible triangles formed by joining vertices of an n – sided regular polygon. if Tₙ₊₁ – Tₙ = 10, then what will be the value of n?
Solution:-
As per the given condition
ⁿ⁺¹C₃ – ⁿC₃ = 10
we know that ⁿCᵣ + ⁿCᵣ ₋ ₁ = ⁿ ⁺ ¹Cᵣ
i.e. ⁿ ⁺ ¹Cᵣ – ⁿCᵣ = ⁿCᵣ ₋ ₁
Hence ⁿC₃ ₋ ₁ = 10
ⁿC₂ = 10
n(n-1) = 20
∴ n = 5 Answer