Is it one way!! For 0C0?? In my book there is written-- each group or selection which can be made by taking some or all of a number of things is called combination! But here things are zero. Is it a way to be considered to choose nothing from nothing?
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Although technically correct, this formulation is not very enlighning. First of all, why is $0!=1$ ? Again, we could say that we have $1$ possibility to arrange $0$ elements. I would choose this way : We have $1!=1$ and $(n+1)!=(n+1)\cdot n!$. This gives $1!=1\cdot 0!$, hence $0!=1$. The definition of the binomial coefficient gives then $$\binom{0}{0}=\frac{0!}{0!\cdot 0!}=\frac{1}{1}=1$$ – Peter Oct 21 '17 at 18:28
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Yes, it is one way. To be precise, nCk is counting the number of $k$-element subsets of an $n$-element set. If $n=k=0$ then we are counting the number of empty subsets of an empty set. There is exactly one such subset: the empty set.
Ted
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