Question

You own 8 CDs. You want to randomly arrange 7 of them in a CD rack. What is the probability that the rack ends up in alphabetical order? Be sure to leave your answer as a fraction in order to earn credit.

Answer 1

STEP - BY - STEP EXPLANATION

What to find?

probability that the rack ends up in alphabetical order.

Given:

Number of CD owns = 8

You are to arrange 7.

To solve we will follow the steps below:

Step 1

Find the total number of possible ways to arrange (i.e all possible outcome).

`Total\text{ number of possible}^{\text{ }}way=^8P_7`
`=(8!)/((8-7)!)`
`=40320`

Step 2

Obtain the required outcome.

Observe that, there would be only one outcome in each selection that would be in alphabetical order

Hence, the required outcome =1

Step 3

Determine the probability.

`Probaility=\frac{required\text{ outcome}}{all\text{ possible outcome}}`
`=(1)/(40320)`

ANSWER

The probability that the rack ends up in alphabetical order = 1/40320