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    Friday, May 28, 2004

    Factorial Friday

    My iPod tells me that I have over 21 days of music loaded. That's an obnoxious 6841 songs. Since I use the shuffle feature regularly, I wonder how many unique 21-day mixes I could make. Ah! Fun with factorials!

    I always enjoyed working with factorials because the math involved is straight-forward. An example is the best definition. Say you have 4 dress shirts to wear throughout the work week (Friday being Hawaiian Shirt Day, of course). And you can't wear the same shirt twice during a given week. So how many different combinations of shirt-wearing do you have?

    The answer is 4 factorial (denoted 4!), or simply 4 x 3 x 2 x 1 = 24 different combinations. You'd have 6 months of different shirt-wearing orders to entertain your colleagues. In other words, a factorial is just a big multiplication party where everyone's invited.

    Now back to the iPod song factorial. We're talking 6841! or 6841 x 6840 x 6839 . . . ad nauseum. That's a hefty calculation! I've tried to get the answer using various online calculators, but all result in the same product: Infinity.

    Anyone want to figure that out for me? And while you're at it, can you explain why 0! = 1?

    [EDIT: Check the comments for the answer. Thanks Chris!]