You own 19 CDs. You want to randomly arrange 6 of them in a CD rack. What is the probability that the rack ends up in alphabetical order?

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There are 19×18×17×16×15×14/(1×2×3×4×5×6)=27,132 different combinations of choosing 6 CDs out of 19. There is nothing in the question to suggest that the 19 CDs are already arranged into alphabetical order.

But, having selected the 6 CDs there are 6!=720 different ways of ordering these and only one would be alphabetical order. The probability is therefore 1/720 (about 0.14%) that they would be in alphabetical order.

It seems irrelevant that there are 19 CDs, because only 6 are chosen to be placed in the rack, and there's only one rack, and the focus of the probability is on the chosen 6.

by Top Rated User (1.2m points)

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