If 5 P(4, n) = 6 P(5, n – 1), find n.

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)}

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