document.write( "Question 1087531: Prove that n combination r is equal to( n combination (n minus r).
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Algebra.Com's Answer #701860 by mathmate(429) $\"\"$ $\"About$

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Question:
\n" ); document.write( "Prove that n combination r is equal to( n combination (n minus r).
\n" ); document.write( " [editorial correction to question, please double check to make sure the corrected question corresponds to the question to be asked ]
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\n" ); document.write( "Solution:
\n" ); document.write( "to prove nCr = nC(n-r)
\n" ); document.write( "proof:
\n" ); document.write( "nCr=n!/(r!(n-r)!) [ by definition of combination ]
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\n" ); document.write( "substitute n-r for r
\n" ); document.write( "nC(n-r) = n!/((n-r)!(n-(n-r))!)
\n" ); document.write( "=n!/((n-r)!(r!))
\n" ); document.write( "=n!/(r!(n-r)!)
\n" ); document.write( "which is exactly the same expression as that for nCr. [QED]
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