Question 1163219
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<pre>

The ratio of these quantities,  nPr and nCr, is  n*(n-1)* . . . *(n-r+1) : {{{(n*(n-1)* ellipsis *(n-r+1))/(r!)}}}  and equals to r!;


so,  r! = {{{336/56}}} = 6.


Hence, r = 3.


Next,  nPr at r = 3 is  n*(n-1)*(n-2) = 336.


After several simple trials and errors you get  n = 8.


You may also use  (n-1) ~ {{{root(3,336)}}} = 6.95 (approx.)


<U>ANSWER</U>.  n = 8,  r = 3.
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Solved.