Given a set $X=\{x_1, \ldots, x_n\}$ I would like to denote the set of all distinct subsets of $X$ which have cardinality $k\le n$.
I am aware that the set of all subsets (of any cardinality) is referred to as the "power set" $\mathcal{P}(X)$. My current intention is to define $\mathcal{P}_k(X)$ the set of subsets with cardinality $k$, such that: $$\mathcal{P}_k(X)=\{Z: Z\subset X, |Z|=k\}$$
Is this appropriate or is there a standard notation for this entity?
This is sometimes denoted by
$$\binom{X}{k} $$
(Inspired obviously from the normal notation for the binomial coefficient)