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Kyle is making a CD containing 10 of his favorite songs. He has chosen

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Bunuel
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Kyle is making a CD containing 10 of his favorite songs. He has chosen [#permalink] New post   29 Apr 2019, 20:58
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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
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Re: Kyle is making a CD containing 10 of his favorite songs. He has chosen [#permalink] New post   29 Apr 2019, 21:32
IMO C


if we fix 2 bule songs at ends ,

we can arrange other 8 songs in 8! ways

and also the two end songs can be arranged in 2! ways

so total no of ways = 8!*2! = 80640


IMO C

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Re: Kyle is making a CD containing 10 of his favorite songs. He has chosen [#permalink] New post   29 Apr 2019, 22:04
The blue songs can be put in the album in 2 ways
The rock n roll songs can be arranged in the album in 8!Ways.
Therefore total number of ways would be 8!*2= 80640
IMO C

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Re: Kyle is making a CD containing 10 of his favorite songs. He has chosen [#permalink] New post   30 Apr 2019, 02:54
Bunuel wrote:
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


CD can be made in 8! * 2 ways
IMO C 80640
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Re: Kyle is making a CD containing 10 of his favorite songs. He has chosen [#permalink] New post   09 Aug 2020, 10:21
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Bunuel wrote:
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


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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Re: Kyle is making a CD containing 10 of his favorite songs. He has chosen [#permalink] New post   10 Aug 2020, 06:18
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Blue songs at the first and last position can be arranged in 2! ways = 2 ways.

Remaining 8 rock-n-roll songs can be arranged (between the blue songs) in 8 ! ways = 40,320

Total ways to order 10 songs = 2*40,320 = 80,640

Answer C
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Re: Kyle is making a CD containing 10 of his favorite songs. He has chosen [#permalink]
10 Aug 2020, 06:18
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