generating arrangements

This is a follow up to my other post that seems much harder to find
information on. I can reduce the total complexity of my problem by atleast
a factor of 10 if instead of generating all permutations on a set I just
generate arrangments.

My question is similar to the other but instead of fast algorithms for
permutations I need it for arrangments(i.e. permutations over subsets).

The simple way, it seems, to attack this problem would be to combine the
algorithms to generate combinations with the ones for generating
permutations so that I first generate a combination then generate the
permutations of that. Does it make sense that if the two methods to
generate the combinations and permutations are relatively fast that when
combined to generate the arrangements it should be fast too? I just can't
find much on arrangement algorithms on google and seems to me that the above
way might be good enough.