Number of Factional Combinations (SMACX)
If you like to solve combinatorial problems, compute the total number of possible combinations of factions in a SMACX game. Assume that either both alien factions must be present or neither (since some early versions allowed a single alien presence). Also assume that the same faction doesn't appear twice in the same game. I've posted my answer below, after some spoiler space.
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First count the number of combinations that include no aliens. That would be choosing 7 factions from 12, which is 12!/(7!5!), or 792. Next, if both alien factions are present, the remaining 5 slots can be filled from any of the twelve non-aliens. That's 12!/(5!7!), which also is 792. The sum 792+792=1584 is the total number of possible combinations.
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