You own 13 CDs. You want to randomly arrange 5 of them in a CD rack. What is the probability that the rack ends up in alphabetical order?

1/154440

Step-by-step explanation:

To calculate the probability it would be the quotient between 1 and the number of ways to choose 5 out of 13, but in this case the order matters, so it would be the permutation 13P5, therefore:

We know that:

nPr = n! / (n-r)!

we replace and we have:

13P5 = 13! / (13-5)! = 154440

The probability  that the rack ends up in alphabetical order is 1/154440

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