1. Calculate the total number of ways to arrange 9 CDs out of 24. This is the number of permutations of 9 CDs, given by:
24P9 = \frac{24!}{(24-9)!} = \frac{24!}{15!}
2. For the arrangement to be in alphabetical order, there is exactly 1 way sinceonlyonespecificorderisalphabetical.
3. The probability that the CDs are in alphabetical order is the number of favorable outcomes 1 divided by the total number of arrangements calculated in step 1:
\frac{1}{\frac{24!}{15!}} = \frac{15!}{24!}
4. Simplify this to get the probability that the CDs are in alphabetical order:
\frac{1}{9!}
Therefore, the final answer is: \frac{1}{9!}=\frac{1}{362880}