Question

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Answer 1

Answer:

Step-by-step explanation:

P(n,5) = n!/(n - 5)!

20P(n,3) = 20n!/(n - 3)!

Equate the two to get

n!/(n - 5)! = 20n!/(n - 3)!

Take the reciprocal of both sides,

(n - 5)!/n! = (n - 3)!/(20n!)

(n - 5)!/n! = (n - 3)(n - 4)(n - 5)!/(20n!)

Divide out (n - 5)!/n!,

1 = (n - 3)(n - 4)/20

(n - 3)(n - 4) - 20 = 0

n² - 7n + 12 - 20 = 0

n² - 7n - 8 = 0

Factor,

(n - 8)(n + 1) = 0

n = -1 is obviously not an answer, so we have n = 8.

Check:

P(8,5) = 6720

P(8,3) = 336

Answer 2

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Refer the attachment.