SOLUTION: hey could you please help me out with this permutation problem: P(n,5)=20P(n,3)

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Question 155008: hey could you please help me out with this permutation problem:
P(n,5)=20P(n,3)

Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!


···

So, 

and 

Substituting,



Get a 0 on the right:



factor out 



Simplify the last parentheses:







Factor the last parentheses:



Setting each factor = 0, we get the
solutions:

, , , , .

The first three are considered correct,
because when , 

And  is a solution.  But the last one
 is not a solution because permutations
are not defined for negative numbers.

So the four solutions are

, , , 

Possibly your teacher may want only
the solution ; however, the first 
three are solutions since they cause 
both sides of the original equation
to equal 0.

Edwin

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