I've been searching for a way to express "the set of all combinations generated by taking $\binom{n}{k}$ items". For example, if I have the set $\{3,7,6,5,9\}$, and I want the set of all sets that are formed by making $\binom{5}{4}$ choices, then the result would be
$\{\{3,7,6,5\}, \{3,6,5,9\}, \{3,7,5,9\}, \{3,7,6,9\}, \{7,6,5,9\}\}$
But I'm struggling to find a notation that describes this. I can describe the number of results with $\binom{5}{4}=5$, but how do I describe the resulting set-of-sets itself? The notation $5 \brace 4$ is already taken by Stirling numbers. I've looked at articles and questions about sets, set theory, the binomial coefficient, and I've drawn a blank.
So, is there a standard notation? (I feel that, surely, there must be!) If there is, what is it? And if there isn't, could anyone suggest a notation that would be halfway familiar to a reader?