Let T<sub>n</sub> denote the number of triangles which can be formed by using the vertices of a regular polygon of n sides. If T<sub>n+1</sub> - T<sub>n</sub> = 21, then n equals:
According to the question we have \[ {}^{n+1}C_3 - {}^nC_3 = 21 \] We know \[ {}^8C_3 - {}^7C_3 = 21 \Rightarrow n = 7 \]
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