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1)

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 the value of n is


A) 7

B) 5

C) 10

D) 8

Answer:

Option B

Explanation:

Given ,   Tn=nC3

   Tn+1=n+1C3

      Tn+1Tn=n+1C3nC3=10(given)

      nC2+nC3nC3=10

                                        (nCr+nCr+1=n+1Cr+1)

      nC2=10n=5