Permute this!
The number of possible permutations of 52 cards is 52!. I think the exclamation mark was chosen as the symbol for the factorial operator to highlight the fact that this function produces surprisingly large numbers in a very short time. If you have an old school pocket calculator, the kind that maxes out at 99,999,999, an attempt to calculate the factorial of any number greater than 11 results only in the none too helpful value of "Error". So if 12! will break a typical calculator, how large is 52!?
52! is the number of different ways you can arrange a single deck of cards. You can visualize this by constructing a randomly generated shuffle of the deck. Start with all the cards in one pile. Randomly select one of the 52 cards to be in position 1. Next, randomly select one of the remaining 51 cards for position 2, then one of the remaining 50 for position 3, and so on. Hence, the total number of ways you could arrange the cards is 52 * 51 * 50 * ... * 3 * 2 * 1, or 52!. Here's what that looks like:
80658175170943878571660636856403766975289505440883277824000000000000
