SOLUTION: How can i show that nPr = (n-1)P(r) + r*[(n-1)P(r-1)

Question 934927: How can i show that nPr = (n-1)P(r) + r*[(n-1)P(r-1)
Answer by Edwin McCravy(20055) (Show Source): You can put this solution on YOUR website!

The permutation formula is 

xPy = 

So we are to prove:

nPr ≟ (n-1)P(r) + r*((n-1)P(r-1)), which becomes:

 ≟ 

 ≟ 

 ≟ 

--------------------------------------------------------------------
Proof:

nPr = 

Now divide  by long division:

                 1                  
           n-r)n+0            
               n-r
                 r

           The quotient is 






nPr = (n-1)P(r) + r
 
Edwin

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