Given: P(n, 5) = 20 P(n, 3)

To find: value of n

We know,

So, according to question:

P(n, 5) = 20 P(n, 3)

⇒ (n – 3) (n – 4) = 20

⇒ n² – 3n – 4n + 12 = 20

⇒ n² – 7n + 12 – 20 = 0

⇒ n² – 7n – 8 = 0

⇒ n² – 8n + n – 8 = 0

⇒ n(n – 8) – 1(n – 8) = 0

⇒ (n – 8) (n – 1) = 0

⇒ n = 8 or 1

For, P(n, r): n ≥ r

∴ n = 8 {for, P(n, 5)}