NP: Combinatorics Ch 3, Q5 page 53, 5th Edition

[aliag916]

Hi, I am having trouble with the explanation to the following question in the NP guide:

The New York Classical Group is designing the liner notes for an upcoming cd release. THere are 10 soloists featured on the album, but the liner notes are only 5 pages long, and therefore only have room for 5 soloists. The soloists are fighting over which of them will appear in the liner notes, though not about which page they appear on. How many different combinations of soloists can appear in the liner notes?

My thinking:
I thought the ans was 10*9*8*7*6/5! because the soloists are not concerned about which page they appear on so the order doesn't matter and hence we got to divide by the 5! ---->the slot method.
If i follow the Anagram method i get YYYYYNNNNN ie 10!/5!5!

However, the strategy guide says the order is imp and lists 2 anagrams ie 12345NNNNN as well as YYYYYNNNNN
and the answer is 10!/5! 5!

But if the anagram is 12345NNNNN and order is important the answer should be 10!/5!.

Please let me know where I've gone wrong in my thinking.
Thank you!
Aliag

[jnelson0612]

Good catch! I can see why you are confused. The answer choice is wrong when it states that the order is important. In fact, the problem tells us that the order is NOT important. In a previous version of this problem, the order was important, and that sentence is probably left over from that answer.

Anyway, your method to solve is correct and matches up with the answer provided. Please just disregard that sentence about the order being important; it clearly is not.

[aliag916]

Thank you Jamie. So would the correction appear in the Errata section of the NP guide so that others don't get confused :)

Thanks!
Aliag

[tim]

only if someone reports the error! go ahead and let them know at http://www.manhattangmat.com/errata.cfm

[aliag916]

Thanks Tim, good idea, Done!

I also believe I've made this post in the wrong forum. It should have been in the Math non CAT forum.

[tim]

that's fine; i didn't notice it either! :)

[tabishsangrar]

Thanks aliag916 and Tim.
I went through the same confusion and it got resolved after reading this post.
So Tim, since the order is not important, we can use 10C5 right?
Coz that's what I've used and it comes up to be same as aliag916's answer.
Just needed confirmation on the use of 10C5 here.

Cheers,
Taz

[jlucero]

Thanks aliag916 and Tim.
I went through the same confusion and it got resolved after reading this post.
So Tim, since the order is not important, we can use 10C5 right?
Coz that's what I've used and it comes up to be same as aliag916's answer.
Just needed confirmation on the use of 10C5 here.

Cheers,
Taz

Correct. 10C5 or 10!/5!5! is the correct formula here. Glad that these forums serve as an errata for our students!

[nocheivyirene]

The New York Classical Group is designing the liner notes for an upcoming cd release. THere are 10 soloists featured on the album, but the liner notes are only 5 pages long, and therefore only have room for 5 soloists. The soloists are fighting over which of them will appear in the liner notes, though not about which page they appear on. How many different combinations of soloists can appear in the liner notes?

Oh! So these things happen! :) 10!/5!5! it is!

[tim]

:)