If P(9, r) = 3024, find r.

1.	If P(9, r) = 3024, find r.
Answer» Given as P (9, r) = 3024 On using the formula, P (n, r) = n!/(n – r)! P (9, r) = 9!/(9 – r)! Therefore, from the question, P (9, r) = 3024 On substituting the obtained values in above expression we get, 9!/(9 – r)! = 3024 1/(9 – r)! = 3024/9! = 3024/(9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1) = 3024/(3024 × 5 × 4 × 3 × 2 × 1) = 1/5! (9 – r)! = 5! 9 – r = 5 -r = 5 – 9 -r = -4 Hence, the value of r is 4.

Answer»

Given as

P (9, r) = 3024

On using the formula,

P (n, r) = n!/(n – r)!

P (9, r) = 9!/(9 – r)!

Therefore, from the question,

P (9, r) = 3024

On substituting the obtained values in above expression we get,

9!/(9 – r)! = 3024

1/(9 – r)! = 3024/9!

= 3024/(9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1)

= 3024/(3024 × 5 × 4 × 3 × 2 × 1)

= 1/5!

(9 – r)! = 5!

9 – r = 5

-r = 5 – 9

-r = -4

Hence, the value of r is 4.

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