Given: P(n, 5) : P(n, 3) = 2 : 1

To find: value of n

We know,

So, according to question:

P(n, 5) : P(n, 3) = 2 : 1

⇒ (n – 3)(n – 4) = 2

⇒ n² – 3n – 4n + 12 = 2

⇒ n² – 7n + 12 – 2 = 0

⇒ n² – 7n + 10 = 0

⇒ n² – 5n – 2n + 10 = 0

⇒ n(n – 5) – 2(n – 5) = 0

⇒ (n – 5) (n – 2) = 0

⇒ n = 5 or 2

For, P(n, r): n ≥ r

∴ n = 5 {∵ P(n, 5)}