Given: P(11, r) = P (12, r – 1)

To find: value of n

We know,

So, according to question:

P (11, r) = P (12, r – 1)

⇒ (13 – r) (12 – r) = 12

⇒ 156 – 12r – 13r + r² = 12

⇒ 156 – 12 – 25r + r² = 0

⇒ r² – 25r + 144 = 0

⇒ r² – 16r – 9r + 144 = 0

⇒ r(r – 16) – 9(r – 16) = 0

⇒ (r – 9) (r – 16) = 0

⇒ r = 9 or 16

For, P(n, r): r ≤ n

∴ r = 9 {for, P(11, r)}