SOLUTION: Prove that n combination r is equal to( n combination (n minus r).

Question 1087531: Prove that n combination r is equal to( n combination (n minus r).

Answer by mathmate(429) (Show Source): You can put this solution on YOUR website!
Question:
Prove that n combination r is equal to( n combination (n minus r).
[editorial correction to question, please double check to make sure the corrected question corresponds to the question to be asked ]

Solution:
to prove nCr = nC(n-r)
proof:
nCr=n!/(r!(n-r)!) [ by definition of combination ]

substitute n-r for r
nC(n-r) = n!/((n-r)!(n-(n-r))!)
=n!/((n-r)!(r!))
=n!/(r!(n-r)!)
which is exactly the same expression as that for nCr. [QED]

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