What is the probability that the CDs are in alphabetical order

Question

You own 23 CDs with different titles. You want to randomly arrange 10 of them in a CD rack. What is the probability that the rack ends up in alphabetical order by title?

Answer 1

No matter which 10 CDs you pick, it is possible to arrange them alphabetically - so it does not matter that there are 23 to choose from. After you have chosen 10 CDs, there is exactly one way that they can be ordered alphabetically. However, there are 10! = 3628800 ways you can possibly arrange those 10 CDs. Thus, the probability of the CDs being arranged alphabetically is 1/3628800.