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Kyle is making a CD containing 10 of his favorite songs. He has chosen two blues songs and 8 rock-n-roll songs to be on

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by VJesus12 » Thu Jul 30, 2020 9:12 am

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Kyle is making a CD containing 10 of his favorite songs. He has chosen two blues songs and 8 rock-n-roll songs to be on the CD. The blues songs will be the first and last songs. How many different orderings of songs on the CD are possible?

A. 3,628,800
B. 161,280
C. 80,640
D. 20,160
E. 160

[spoiler]OA=C[/spoiler]

Source: Princeton Review
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Re: Kyle is making a CD containing 10 of his favorite songs. He has chosen two blues songs and 8 rock-n-roll songs to be

by Scott@TargetTestPrep » Wed Aug 05, 2020 10:01 am
VJesus12 wrote: ↑
Thu Jul 30, 2020 9:12 am
 Kyle is making a CD containing 10 of his favorite songs. He has chosen two blues songs and 8 rock-n-roll songs to be on the CD. The blues songs will be the first and last songs. How many different orderings of songs on the CD are possible?

A. 3,628,800
B. 161,280
C. 80,640
D. 20,160
E. 160

[spoiler]OA=C[/spoiler]

Solution:

There are 2! ways to put the 2 blues songs at either end of the list and there are 8! ways to put the 8 rock-n-roll songs in between the 2 blues songs. Therefore, there are 2! x 8! = 80,640 different orderings of songs on the CD.

Answer: C

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