<PRE><B>Question 1147834</B>
&lt;br&gt;
The difference between nPr and nCr is a factor of r! in the denominator for nCr:&lt;br&gt;
{{{nCr = nPr/r!}}}&lt;br&gt;
So&lt;br&gt;
{{{r! = nPr/nCr = 3024/126 = 24}}}&lt;br&gt;
So r is 4.&lt;br&gt;
So nPr = 3024 is the product of four consecutive integers.  Find the integers by looking at the prime factorization of 3024 and grouping the prime factors to form those four integers.&lt;br&gt;
{{{3024 = (2^4)(3^3)(7)}}}&lt;br&gt;
Clearly one of the four integers is 7.&lt;br&gt;
And there is no factor of 5, so neither 5 nor 10 can be one of the integers.&lt;br&gt;
Therefore the four integers are 6, 7, 8, and 9; so n is 9.&lt;br&gt;
ANSWER: n=9; r=4</PRE>