To the OP - be careful with this, because given X particles and X! possible ways to arrange those particles it does not necessarily mean that the one arrangement that actually exists is a long shot. Think about this - if you thoroughly shuffle a deck of cards there are 52! arrangements that the deck can end up in. That's a huge number - but that does not mean that the arrangement you actually get when you shuffle a deck is somehow "special." Only when you pre-define a particular arrangement of cards, then shuffle the deck and get that one arrangement is it remarkable.