SOLUTION: Determine the value of n which make the following statment true: (1/2) nP7= n-2P5

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Question 234708: Determine the value of n which make the following statment true:
(1/2) nP7= n-2P5
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Determine the value of n which make the following statment true:
(1/2) nP7= n-2P5
(1/2)n!/(n-7)! = (n-2)!/(n-7)!
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The denominators are equal so equate the numerators:
(1/2)n! = (n-2)!
Divide both sides by (n-2)!
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(1/2)n(n-1) = 1
n(n-1) = 2
n^2-n-2 = 0
(n-2)(n+1) = 0
Positive solution:
n = 2
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Hmmmm? That answer does not make sense because
you cannot have 2P7 in the original equation.
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Cheers,
Stan H.