If P (5, r) = P (6, r – 1), find r.

Given: P (5, r) = P (6, r – 1)

To find: value of r

We know,

So, according to question:

P (5, r) = P (6, r – 1)

⇒ (7 – r) (6 – r) = 6

⇒ 42 – 6r – 7r + r² = 6

⇒ 42 – 6 – 13r + r² = 0

⇒ r² – 13r + 36 = 0

⇒ r² – 9r – 4r + 36 = 0

⇒ r(r – 9) – 4(r – 9) = 0

⇒ (r – 9) (r – 4) = 0

⇒ r = 9 or 4

For, P(n, r): r ≤ n

∴ r = 4 {for, P(5, r)}