Question 1147834
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nPr = n*(n-1)*(n-2)*(n-r+1).


nCr = {{{(n*(n-1)*(n-2)*(n-r+1))/r!}}}.


So the ratio  nPr/nCr is  r!, and it is equal to  {{{3024/126}}} = 24.


It implies  r = 4.


Then  nPr = n*(n-1)*(n-2)*(n-3) = 3024.


I made a short table using MS Excel in my computer


    n       n*(n-1)*(n-2)*(n-3)

    4		24
    5		120
    6		360
    7		840
    8		1680
    9		3024
   10		5040


which shows that  n= 9.


<U>ANSWER</U>.  r = 4;  n = 9.
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Solved.



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