nP4=20(nP2) then find the value of n

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Solution

nP4=20nP2

nP4 = n!/(n-4)! = n(n-1)(n-2)(n-3)*(n-4)!/(n-4)! = n(n-1)(n-2)(n-3)
nP2 = n!/(n-2)! = n(n-1)

n(n-1)(n-2)(n-3) = 20n(n-1)
(n-2)(n-3) = 20
n² - 5n + 6 = 20
n² - 5n - 14 = 0
(n+2)(n-7) = 0
n = -1, 7

Discard the n < 4 result
n = 7

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