I'm having two sets like
$S_1 = \{ A, B, C \}$
$S_2 = \{ D, E\}$
Within each Set I can form all possible combinations, so A,B,C,AB,AC,BC,ABC in the first case, which sums up to $2^n-1$ possibilities if I leave out zero (7 for $S_1$ and 3 for $S_2$).
However, now I'm looking for a formula to compute the number of different combinations for two (or several sets), but where I'm only allowed to take at most 1 (so 0 or 1) elements from each set. So in the example above I could take AD or CE as well as A or just D, but no AB, ABD or ADE - only no more than 1 element from the different sets.
What's a universal formula for this?
Any help is appreciated! Thanks!