document.write( "Question 1077089: nC12 = nC8, find n, then find the value of nC17 \n" ); document.write( "
Algebra.Com's Answer #692395 by Edwin McCravy(20059)\"\" \"About 
You can put this solution on YOUR website!
\"matrix%281%2C3%2CnC12%2C%22%22=%22%22%2CnC8%29\"\r\n" );
document.write( "\r\n" );
document.write( "If you know that \"matrix%281%2C3%2CnCr%2C%22%22=%22%22%2CnC%28n-r%29%29\", then\r\n" );
document.write( "it's easy.\r\n" );
document.write( "\r\n" );
document.write( "r = 12,  n-r = 8\r\n" );
document.write( "        n-12 = 8\r\n" );
document.write( "           n = 20\r\n" );
document.write( "\r\n" );
document.write( "Otherwise:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Cross-multiply:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Divide both sides by n!\r\n" );
document.write( "\r\n" );
document.write( "\"matrix%281%2C3%2C8%21%28n-8%29%21%2C%22%22=%22%22%2C12%21%28n-12%29%21%29\"\r\n" );
document.write( "\r\n" );
document.write( "Write 12! as 12∙11∙10∙9∙8!\r\n" );
document.write( "\r\n" );
document.write( "\"matrix%281%2C3%2C8%21%28n-8%29%21%2C%22%22=%22%22%2C12%2A11%2A10%2A9%2A8%21%28n-12%29%21%29\"\r\n" );
document.write( "\r\n" );
document.write( "Divide both sides by 8!\r\n" );
document.write( "\r\n" );
document.write( "\"matrix%281%2C3%2C%28n-8%29%21%2C%22%22=%22%22%2C12%2A11%2A10%2A9%28n-12%29%21%29\"\r\n" );
document.write( "\r\n" );
document.write( "Write (n-8)! as (n-8)∙(n-9)∙(n-10)∙(n-11)∙(n-12)!\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Divide both sides by (n-12)!\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "n-8=12, n-9=11, n-10=10, n-11=9\r\n" );
document.write( "  n=20,   n=20,    n=20,    n=20\r\n" );
document.write( "\r\n" );
document.write( "Answers: \"n+=+20\",  \"nC17+=+20C17+=+20C3+=+%2820%2A19%2A18%29%283%2A2%2A1%29=1140\"\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );