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)}