Please excuse me if this question is too juvenile for this forum. Actually weirdly I cant figure this out.
I have 3 letters $A, B, C$ I need a formula that gives me all the possible arrangements for this like: $$ A, B, C\\ AB, BC, CA\\ ABC $$ Note, the order is not important and I want to exclude the duplicated like $CA$ and $AC$. I need this for $n$ letters.
Sorry again and I am really ashamed to be asking this question here ;)
On
If you are looking for the number of all possible "arrangements" per your criteria, then your problem is equivalent to finding the number of non-empty subsets of a set of three elements $\{A, B, C\}$.
This is equivalent to the cardinality of the powerset of the set, minus the empty set, where the powerset of a set $S$, $P(S)$ is the set of all subsets of $S$.
So your answer will $$|P(S)| - 1 = 2^n -1$$
Try $$(1+A)(1+B)(1+C)=1+A+B+C+AB+AC+BC+ABC$$
and extend it to $n$...