Sometimes we can literally count the number of ways you can reshuffle a series of bits - as with a pack of cards, for instance, where the 'bits' are the individual cards.
Suppose the dealer shuffles the pack and deals them out to four players, so that they each have 13 cards. I pick up my hand and gasp in astonishment. I have a complete hand of 13 spades! All the spades.
I am too startled to go on with the game, and I show my hand to the other three players, mowing they will be as amazed as I am.
i of the other players lays his cards on the table, and the gasps of astonishment grow with each hand. Every one of them has a Z perfect' hand: one has 13 hearts, another has 13 diamonds, and the last one has 13 clubs.
Would this be supernatural magic? We might be tempted to think so. Mathematicians can calculate the chance of such a remarkable deal happening purely by chance. It turns out to be almost impossibly small: 1 in 536,447,737,765,488,792,839,237,440,000. I'm not sure I would even know how to say that number! If you sat down and played cards for a trillion years, you might on one occasion get a perfect deal like that. But - and here's the thing - this deal is no more unlikely than every other deal of cards that has ever happened! The chance of any particular deal of 52 cards is 1 in 536,447,737,765,488,792,839,237,440,000 because that is the total number of all possible deals. It is just that we don't notice any particular pattern in the vast majority of deals that are made, so they don't strike us as anything out of the ordinary. We only notice the deals that happen to stand out in some way.