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Let Tn be the number of all possible triangles formed by joining vertices of an n-sided regular polygon. If Tn+1Tn = 10, then the value of n is

Solution :

Given, Tn = nC3

Tn+1 = n+1C3

T_{n+1}T_n = ^{n+1}C_3  – ^{n}C_3  = 10  [given]

\therefore ^nC_2 + ^nC_3^nC_3 = 10

\implies ^nC_2 = 10

\therefore n = 5


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