Dangling Conversations

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Rampant innumeracy

Posted 12 Jan, 2005 at 13:41 by matt in /Math | Permanent link

Apple, j'accuse!

One of the taglines for the new iPod shuffle: "240 songs. A million different ways." Now, not considering for the moment whether an MP3 player with no playlist display is really a smart direction -- after all, it's not like Apple's is the first one -- my mathematical sense is highly offended by their slogan.

The total number of ways of ordering 240 objects is 240!, which is, um, not a small number. A very big number, in fact. Roughly, it's 4.07×10468. (Thank you, Mathematica.) So saying that there are "a million different ways" (not even "at least"!) is a criminal understatement. For comparison, if you want to have a million different ways: get yourself a portable CD player, find a CD with ten tracks on it, and hit "shuffle". (Even then you're overshooting the mark by a factor of 3.6 or so, but at least you're in the right ballpark.)

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