counting the number of ordered subsets in a n-set is easy, it's $ 2 ^n -1 $ (assuming we don"t want the empty subset, it's the sum of $ n \choose i $ , i>0
now imagine I have a set s=(a, b, x), where x can have 2 possible values x1, x2
the result wanted:
(a), (b), (x1), (x2), (a,b), (a,x1), (a,x2), (b,x1), (b,x2), (a,b,x1), (a,b,x2)
I would like to generalize with s of length n, and x having k possible values
=> Counting the subsets of $ (a_1, a_2, a_3, ...,a_{n-1}, \begin{matrix} x_1\\ x_2 \\ \vdots\\ x_k \end{matrix} ) $