Algorithm to generate combinations of n elements from n sets of m elements


Suppose I have 3 sets of 2 elements: [A, B], [C, D], [E, F], and I wanted to generate all possible combinations of 1 element from each set, such that the result of the algorithm would be:

[A, C, E], [A, C, F], [A, D, E], [A, D, F], [B, C, E], [B, C, F], [B, D, E], [B, D, F] 

What algorithm can I use to generate all combinations. Keep in mind that I’m looking for an algorithm that will work on any number of sets that have any number of elements, the above is just an example. Also, remember that I’m looking for an algorithm to actually generate the combinations, not just count them.