SOLUTION: Prove that nCr=nC(n-r).

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Question 1019557: Prove that nCr=nC(n-r).
Found 2 solutions by Alan3354, mathmate:
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
Prove that ncr = ncn-r .
===========
In general, they're not equal.

Answer by mathmate(429)   (Show Source): You can put this solution on YOUR website!

Question:
Prove that nCr=nCn-r.

Solution:
By definition,
nCr=
Substitute n-r for r, then
nCn-r
=
=
= [by commutativity of multiplication]

Since the simplified expressions of
nCr and nCn-r are equivalent, therefore nCr=nCn-r.

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