"All the stuff with permutations has emphasized order. Somebody gets first place in the golf tournament, and somebody else gets second, and you bet your bottom dollar that it matters which is which. What if it turns out we don’t care about the order, though? Maybe we don’t care who got what place, but just which golfers were in the top ten. Maybe we don’t care which film is showing in which time slot, but only which films are in tonight’s movie lineup. This counting scenario involves something called combinations rather than permutations. A combination of k objects out of a possible n is a choice of any set of k of them, without regard to order. For instance, suppose all three Davies kids want to play on the Wii, but only two can play at a time. Who will get to play first after school? One possibility is Lizzy and T.J., another is Lizzy and Marina, and the last one is T.J. and Marina. These are the three (and only three) combinations of 2 objects out of 3."