You own 15 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?

the probability that the cds are in alphabetical order is

The first important observation to make is that owning 15 CDs is irrelevant.  The 9 CDs that are not chosen do not affect the rack.  We care only about the six CDs on the rack.

Then, observe that there are ways to arrange the six CDs.  This is because there are six ways to pick the first CD to put in the first position, then five ways to pick the next one in line, then four for the one after that, and so on.

Finally, note that there is only one arrangement in alphabetical order.  (For the sake of simplicity, I'll assume none of the CDs have the same name, and thus that there is a unique arrangement for alphabetical order.)

Therefore, there is one working arrangement and possible arrangements, leading to as our probability.

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