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]
