Given: 5 P(4, n) = 6 P(5, n – 1)

To find: value of n

We know,

So, according to question:

5 P(4, n) = 6 P(5, n – 1)

⇒ (6 – n) (5 – n) = 6

⇒ 30 – 6n – 5n + n² = 6

⇒ 30 – 6 – 11n + n² = 0

⇒ n² – 11n + 24 = 0

⇒ n² – 8n – 3n + 24 = 0

⇒ n(n – 8) – 3(n – 8) = 0

⇒ (n – 8) (n – 3) = 0

⇒ n = 8 or 3

For, P(n, r): r ≤ n

∴ n = 3 {for, P(4, n)}