If I have $m$ $k$-tuples, how many combinations of a single element from the $k$-tuple are possible?
Concrete example:
If I have 6 2-tuples of the form $(a_1, b_1),(a_2, b_2), ... ,(a_6, b_6) $, and the stipulation that I can only draw one element from each tuple (so if I select $a_1$ I can no longer select $b_1$), how many combinations of $a_i$ and $b_i$ are possible?
Edit: You must select an element from each tuple.