> So, my problem with how this is modeled is it assumes order doesn't matter in one aspect, but that it does in another.

Yeah, I'm with you here. Assuming heads=girl and tails=boy:

* If order does NOT matter (GB=BG), then it means Alice-Albert (GB, Heads-Tails) is the same as Albert-Alice (BG, Tails-Heads).

* If order DOES matter (GB!=BG), then it means Alice-Barbara (GG, Heads-Heads) is different than Barbara-Alice (GG, Heads-Heads). Thereforce, GG!=GG.

Either way, the stated problem seems badly defined.