nP2 + nC2 = 84
\(∴\frac{ni}{(n-2i)}+\frac{ni}{2i(n-2)i}\)
\(∴ \frac{ni}{(n-2)i}[1 + \frac{1}{2}] =84\)
\(∴ \frac{n(n-1)(n-2)i}{(n-2)i}[\frac{3}{2}] = 84\)
∴ n(n – 1) = 84 × 23
∴ n(n – 1) = 28 × 2
∴ n(n – 1) = 56
∴ n(n – 1) =8 × 7
∴ n(n – 1) = 8(8 – 1)
∴ n = 8