document.write( "Question 920291: Show that r(nCr) = n[(n-1)C(r-1)] \n" ); document.write( "
Algebra.Com's Answer #558286 by Edwin McCravy(20054)\"\" \"About 
You can put this solution on YOUR website!
\"r%2A%28nCr%29\"\"%22%22=%22%22\"\"n%2A%28%22%28n-1%29%22%5B%22%22%5D%2AC%28r-1%29%29\"
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document.write( "By definition \"ACB+=+A%21%2F%28B%21%28A-B%29%21%29\"\r\n" );
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document.write( "\"r%2A%28n%21%2F%28r%21%28n-r%29%21%29%29\"\"%22%22=%22%22\"\"n%2A%28%28n-1%29%21%2F%28%28r-1%29%21%28n-1-%28r-1%29%29%21%29%29\"\r\n" );
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document.write( "\"r%2A%28n%21%2F%28r%21%28n-r%29%21%29%29\"\"%22%22=%22%22\"\"n%2A%28%28n-1%29%21%2F%28%28r-1%29%21%28n-1-r%2B1%29%21%29%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"r%2An%21%2F%28r%21%28n-r%29%21%29\"\"%22%22=%22%22\"\"%28n%2A%28n-1%29%21%29%2F%28%28r-1%29%21%28n-r%29%21%29\"\r\n" );
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document.write( "Write the r! in the denominator on the left as r(r-1)!\r\n" );
document.write( "Write the n*(n-1)! in the numerator on the right as n!\r\n" );
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document.write( "\"r%2An%21%2F%28r%2A%28r-1%29%21%28n-r%29%21%29\"\"%22%22=%22%22\"\"n%21%2F%28%28r-1%29%21%28n-r%29%21%29\"\r\n" );
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document.write( "Cancel the r's on the left:\r\n" );
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document.write( "\"cross%28r%29%2An%21%2F%28cross%28r%29%2A%28r-1%29%21%28n-r%29%21%29\"\"%22%22=%22%22\"\"n%21%2F%28%28r-1%29%21%28n-r%29%21%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"n%21%2F%28%28r-1%29%21%28n-r%29%21%29\"\"%22%22=%22%22\"\"n%21%2F%28%28r-1%29%21%28n-r%29%21%29\"\r\n" );
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document.write( "Both sides are now the same.\r\n" );
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document.write( "Edwin
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