Given: P(n, 4) = 12. P(n, 2)

To find: value of n

We know,

So, according to question:

P(n, 4) = 12 P(n, 2)

⇒ (n – 2) (n – 3) = 12

⇒ n² – 3n – 2n + 6 = 12

⇒ n² – 5n + 6 – 12 = 0

⇒ n² – 5n – 6 = 0

⇒ n² – 6n + n – 6 = 0

⇒ n(n – 6) – 1(n – 6) = 0

⇒ (n – 6) (n – 1) = 0

⇒ n = 6 or 1

For, P(n, r): n ≥ r

∴ n = 6 {for, P(n, 4)}