SOLUTION: Proof that ncr=(n/n-r)(n-1 c r) Proof that n(n-1 c r) = (r+1) (n c r+1)

Question 1107228: Proof that ncr=(n/n-r)(n-1 c r)
Proof that n(n-1 c r) = (r+1) (n c r+1)
Answer by math_helper(2461) (Show Source): You can put this solution on YOUR website!
Part I
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(by definition)

=
We can bring the n into the factorial in the numerator to go from (n-1)! to n!,
and similarly we can bring in the (EDIT: n-r) in the denominator to go from (n-1-r)! to (n-r)! :
= DONE.
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Part II
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LHS: nC(n-1,r) =
RHS: (r+1)C(n,r+1) =
=
Canceling (r+1) from numerator and denominator:
= = LHS, DONE

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