Given a collection of finite sets, how might one think about finding the set (unordered) of all systems of distinct representatives for the collection?
Example:
$S$: {{1, 2}, {1, 2, 3}}
Unordered SDRs: {{1, 2}, {1, 3}, {2, 3}}
Notice that {2, 1} is already counted by "{1, 2}" as the SDRs are unordered.
System of Distinct Representatives Definition:
Let $S=(S_1,S_2,...,S_n)$ be a collection of sets. A System of Distinct Representatives (SDR) of $S$ is a collection of elements $x_1,x_2,...,x_n$ such that $x_i∈S_i$ and $x_i≠x_j$ for all $i,j∈\{1,2,...,n\}$ where $i≠j$