Saturday, March 3, 2012

Continuing on the theme of probability, suppose you have 12 songs on a CD and you want to play them in random order. How many ways can those songs be played and what is the probability that the song order on the CD will be the order played?

The song order on the CD is only 1 possible way the songs can be played. The probability is then 1 divided by the number of possible ways all songs could be played.

Have 12 slots, each representing a song selection  ___  ____ ____ ___ ___ ___ ___ ___ ___ ___ ___ ___

In the first spot, any of the 12 songs could be played, then in the second spot any of the remaining 11 songs could be played, in the next spot any of the remaining 10 songs could be played and so on.  Therefore the possible ways the songs could be played is 12 * 11 * 10 * 9 ..... * 1.  This is represented as 12!.  The probability is then 1/12!

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