I was wondering what "nC0", or taking n objects zero times at once, really means. I could not really find an answer to this elsewhere, except for a place which sort of represented this as the number of sets containing zero elements. Sort of like the empty set which is there always. I could only faintly connect to this idea though; a much clearer explanation would be much appreciated.
Edit: Seems I should have asked this in a better way. As I say in a comment, I am not much into mathematical definitions, I was just thinking of it in a practical way, like if I have "n" things how do I choose from them while taking none of them in any case. What "nC0" would represent in such situations is what drove me to ask this question.
Edit 2: My doubt has been clarified, thanks @5xum :)
$${n\choose k}$$ denotes the number of $k$-sized subsets of a $n$-sized subset. That is, taking a set $A$ such that $|A|=n$, the number of distinct subsets of $A$ which have $k$ elements is ${n\choose k}$. Since the particular elements of $A$ do not matter, we can therefore say that $${n\choose k} = \left|\{X\subseteq\{1,2,\dots, n\}| |X| = k\}\right|$$
Therefore, ${n\choose 0}$ is the number of subsets of $A$ that have size $0$. There is only one such set, the empty set $\emptyset$, that is, for every $n$, we have $${n\choose 0} = \left|\{X\subseteq\{1,2,\dots, n\}| |X| = 0\}\right|=|\{\emptyset\}| = 1$$ therefore, for every $n$, we have $${n\choose 0} = 1$$