We Only Notice Certain Statistical Events

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 ...