document.write( "Question 1147834: given nPr=3024 and nCr=126 find n and r \n" ); document.write( "
Algebra.Com's Answer #769155 by ikleyn(52781)\"\" \"About 
You can put this solution on YOUR website!
.
\n" ); document.write( "
\r\n" );
document.write( "\r\n" );
document.write( "nPr = n*(n-1)*(n-2)*(n-r+1).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "nCr = \"%28n%2A%28n-1%29%2A%28n-2%29%2A%28n-r%2B1%29%29%2Fr%21\".\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "So the ratio  nPr/nCr is  r!, and it is equal to  \"3024%2F126\" = 24.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "It implies  r = 4.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Then  nPr = n*(n-1)*(n-2)*(n-3) = 3024.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "I made a short table using MS Excel in my computer\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    n       n*(n-1)*(n-2)*(n-3)\r\n" );
document.write( "\r\n" );
document.write( "    4		24\r\n" );
document.write( "    5		120\r\n" );
document.write( "    6		360\r\n" );
document.write( "    7		840\r\n" );
document.write( "    8		1680\r\n" );
document.write( "    9		3024\r\n" );
document.write( "   10		5040\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "which shows that  n= 9.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "ANSWER.  r = 4;  n = 9.\r\n" );
document.write( "
\r
\n" ); document.write( "\n" ); document.write( "Solved.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );