In terms of conventional set notation, a set and it's corresponding power set of cardinality $2$ can be defined:
\begin{align} &A&=\quad&\{a,b,c,d\}&\\ &\mathcal{P}_{2}(A)&=\quad&\{\{a,b\},\{a,c\},\{a,d\},\{b,c\},\{b,d\},\{c,d\}\}&\\ \end{align}
What is the convention for defining the product of all subsets $\{ab,ac,ad,bc,bd,cd\},$ and the sum of these products $\{ab+ac+ad+bc+bd+cd\}$?
Clearly they can be defined with $\prod$ and $\sum$ notation, but this becomes cumbersom for larger cardinalities of power sets.
We can use the "$n$ choose $r$" notation, say $\binom{A}{2}$, then for the sum we can write $\sum_{\{a,b\}\in\binom{A}{2}}ab$.