Question

You own 11 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

Answer 1

To find the probability that the CDs end up in alphabetical order, we need to determine the total number of possible arrangements and the number of arrangements that result in alphabetical order. The probability is 0.0022 (rounded to four decimal places).

Step-by-step explanation:

To find the probability that the CDs end up in alphabetical order, we need to determine the total number of possible arrangements and the number of arrangements that result in alphabetical order.

There are 11 CDs and we need to select 5 of them to put in the CD rack. The total number of possible arrangements is given by the combination formula, which is 11 choose 5.

To determine the number of arrangements that result in alphabetical order, we can consider the number of ways the first CD can be chosen, the number of ways the second CD can be chosen, and so on. For example, if the first CD is A, there are 10 remaining CDs to choose from for the second CD, 9 for the third CD, and so on.

Therefore, the probability that the rack ends up in alphabetical order is the number of arrangements resulting in alphabetical order divided by the total number of possible arrangements.

Let's calculate the probability:

1. Calculate the total number of possible arrangements: 11 choose 5 = 462
2. Calculate the number of arrangements resulting in alphabetical order: There is only one way for the CDs to be in alphabetical order.
3. Calculate the probability: Probability = (Number of arrangements resulting in alphabetical order) / (Total number of possible arrangements) = 1 / 462 = 0.0022 (rounded to four decimal places)