TITLE: Notation for the set created from the combination or permutation of a set
QUESTION [15 upvotes]: For a set $S$ with $n$ elements, the notation for a combination $\binom{n}{k}$, or $C(n, k)$, indicates the number of combinations of $k$ elements from $S$, but how does one indicate the actual set created from combinations of $k$ elements from $S$? That is, $\binom{n}{k}$ is the size of the set I'd like to represent.
Likewise, how would one indicate the actual set of items created from the permutations of $k$ elements, rather than the size of that set?

REPLY [2 votes]: A common notation for the collection of all size-$k$ subsets of $S$ is given by the symbol $S_k$.