Yes, BrowserUk you are right... we can go from a super duper wildly humongous number to just a super duper humongous number. There is a heck of a lot that I don't understand about the requirements to this OP.

There is presumably some "test" that will be done on these combinations, which the OP does not mention. Whatever that "test" is, it is bound to take some MIPS and probably a significant number of them!

Without some more information as to the actual problem that the OP is trying to solve, I do not see any brute force calculation tactics that can do the required math to produce an "optimal solution". I suspect that a better description of the problem could potentially lead to a plausible, "pretty good" rather than an "optimal solution" with many orders less of processing power. Absent that, I am out of ideas.