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how do I solve:

 

nP6 = 5(nP5)

 

thanks!

 Jun 11, 2019
 #1
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P (n, 6)  = 5P(n, 5)       we have

 

    n!                 5 n!

_______  =      _______       divide out n!

 (n - 6)!             (n - 5)!

 

   1        =       5

____           _______          cross-multiply

(n - 6)!         (n - 5)!

 

(n - 5)!  = 5(n - 6)!       Note that we can write (n - 5)!   as (n - 5) (n - 6)!

 

 

(n -5) (n - 6)!  = 5(n - 6) !       divide both sides by   (n - 6)!

 

n - 5  = 5

 

n = 10

 

Proof

 

P(10, 6)  = 151,200

5P(10 - 5) = 151,200

 

cool cool cool

 
 Jun 11, 2019

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