SOLUTION: how would a person prove the result algebraically of this problem nCr = nCn-r and explain why it must be true using a Pascals Triangle.

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Question 380103: how would a person prove the result algebraically of this problem nCr = nCn-r
and explain why it must be true using a Pascals Triangle.
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
Algebraically they're equivalent, it's very simple to prove:
nCr+=+n%21%2F%28%28n-r%29%21r%21%29
nC%28n-r%29+=+n%21%2F%28%28n-%28n-r%29%29%21%28n-r%29%21%29+=+n%21%2Fr%21%28n-r%29%21+=+nCr
It's also true because Pascal's triangle is symmetric.