# 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)}

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