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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?

user160623
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    The word multiset ordinarily means a collection of items which may appear with repetitions. So describing a collection as a multiset of distinct subsets is unclear. – hardmath Nov 20 '23 at 12:56

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This is sometimes denoted by

$$\binom{X}{k} $$

(Inspired obviously from the normal notation for the binomial coefficient)

Carlyle
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