I was enumerating the elements of the power set of this set $S:= \{1,2,3,4,5\}$ and I thought that the number of these elements could be obtained with this: $$\#\wp S = 1 + \sum_{k=1}^n {n\choose k}$$ where $n=\#S$
I saw that it holds for this set. But I'm not sure what if it could be applied to a different kind of set.