For the most part the comments so far are:
- people misunderstanding the problem (which is not surprising; it's the sort of problem mathematicians are better at understanding than the general population, and the audience there is not necessarily mathematicians);
- programmer types whining "waah, this problem is in NP, I can't do it!". Is it in NP? I don't feel like thinking about that -- but I did it in a few minutes, and more importantly with a couple seconds of computation time. NP doesn't stand for "not possible";
- people saying "who cares, most of those combinations are politically unrealistic!" (which I have to admit is true);
- a few estimates of the answer based on some quick and dirty statistical assumptions, which look basically right;
- and a couple people (me included) who have gotten a numerical answer.
What's interesting to see is that a lot of people seem to believe you have to actually generate the sets in order to count them. That would of course be hopeless. The explanation of combinatorics as "counting without counting" comes to mind.