# 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

## Solution :

Given, $$T_n$$ = $$^nC_3$$

$$T_{n+1}$$ = $$^{n+1}C_3$$

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

$$\therefore$$ $$^nC_2$$ + $$^nC_3$$ – $$^nC_3$$ = 10

$$\implies$$ $$^nC_2$$ = 10

$$\therefore$$ n = 5

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