Permutation and CombinationMedium
Question
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 :
Options
A.7
B.5
C.10
D.8
Solution
Tn = nC3 ⇒ n+1C3 - nC3 = 10
(n + 1) n (n - 1) - n(n - 1) (n - 2) = 60
n(n - 1) = 20
n = 5
(n + 1) n (n - 1) - n(n - 1) (n - 2) = 60
n(n - 1) = 20
n = 5
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