SOLUTION: proof of zero factorial

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Question 378803: proof of zero factorial
Found 2 solutions by rapaljer, robertb:
Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
You can't PROVE that 0! is 1. 0!=1 by DEFINITION. There is no proof.

Dr. Rapalje

Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
0! = 1.
This is not a proof, but just an explanation. The number of ways of selecting r objects out of n objects regardless of order, r%3C=n, is given by nCr+=+%28n%21%29%2F%28r%21%28n-r%29%21%29. If r = n, it is equivalent to selecting all objects at one time. The number of ways of doing that is 1. Hence nCn+=+%28n%21%29%2F%28n%21%28n-n%29%21%29+=+1, or %28n%21%29%2F%28n%210%21%29+=+1, or 1%2F0%21+=+1. Thus 0! = 1.