document.write( "Question 1147834: given nPr=3024 and nCr=126 find n and r \n" ); document.write( "

Algebra.Com's Answer #769181 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "The difference between nPr and nCr is a factor of r! in the denominator for nCr:

\n" ); document.write( " $\"nCr+=+nPr%2Fr%21\"$

\n" ); document.write( "So

\n" ); document.write( " $\"r%21+=+nPr%2FnCr+=+3024%2F126+=+24\"$

\n" ); document.write( "So r is 4.

\n" ); document.write( "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.

\n" ); document.write( " $\"3024+=+%282%5E4%29%283%5E3%29%287%29\"$

\n" ); document.write( "Clearly one of the four integers is 7.

\n" ); document.write( "And there is no factor of 5, so neither 5 nor 10 can be one of the integers.

\n" ); document.write( "Therefore the four integers are 6, 7, 8, and 9; so n is 9.

\n" ); document.write( "ANSWER: n=9; r=4 \n" ); document.write( "

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