To approximate 52! by hand, compute 54! and divide by 3000
No discussion of 52! is complete without [1]. A somewhat condensed version of one of the illustrations from the site.<p><i>52! is the number of different ways you can arrange a single deck of cards. Let's try to wrap our puny human brains around the magnitude of this number with a fun little theoretical exercise. Start a timer that will count down the number of seconds from 52! to 0. We're going to see how much fun we can have before the timer counts down all the way.
Start by picking your favorite spot on the equator. You're going to walk around the world along the equator, but take a very leisurely pace of one step every billion years. Make sure to pack a deck of playing cards, so you can get in a few trillion hands of solitaire between steps.<p>After you complete your round the world trip, remove one drop of water from the Pacific Ocean. Now do the same thing again: walk around the world at one billion years per step, removing one drop of water from the Pacific Ocean each time you circle the globe. Continue until the ocean is empty.<p>When it is, take one sheet of paper and place it flat on the ground. Now, fill the ocean back up and start the entire process all over again, adding a sheet of paper to the stack each time you’ve emptied the ocean. Do this until the stack of paper reaches from the Earth to the Sun.<p>Take a glance at the timer, you will see that the three left-most digits haven’t even changed. You still have 8.063 × 10⁶⁷ more seconds to go. So, take the stack of papers down and do it all over again. One thousand times more. Unfortunately, that still won’t do it. There are still more than 5.385 × 10⁶⁷ seconds remaining. You’re just about a third of the way done.</i><p>[1] <a href="http://czep.net/weblog/52cards.html" rel="nofollow">http://czep.net/weblog/52cards.html</a>