^{n}P_{2} + ^{n}C_{2} = 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