Let Tn be the number of all possible triangles formed by joining vertices of an n‑sided regular polygon. If Tn+1

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Mathematics

Permutation and Combination Basic Definitions

Question

Let T_n be the number of all possible triangles formed by joining vertices of an n‑sided regular polygon.

If T_n+1 – T_n = 10, then the value of n is :

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T_n = ⁿC₃ $\Rightarrow$ T_n+1 = ⁿ⁺¹C₃

T_n+1 – T_n = 10 $\Rightarrow$ ⁿ⁺¹C₃ – ⁿC₃ = 10

ⁿC₂ = 10

n = 5