In how many ways can 11 books on English and 9 books on : GMAT Problem Solving (PS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 16 Jan 2017, 19:20

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# In how many ways can 11 books on English and 9 books on

Author Message
TAGS:

### Hide Tags

Intern
Joined: 27 Nov 2009
Posts: 2
Followers: 0

Kudos [?]: 4 [3] , given: 2

In how many ways can 11 books on English and 9 books on [#permalink]

### Show Tags

27 Nov 2009, 13:40
3
KUDOS
1
This post was
BOOKMARKED
00:00

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 100% (02:02) wrong based on 10 sessions

### HideShow timer Statistics

In how many ways can 11 books on English and 9 books on French be placed in a row on a shelf so that two books on French may not be together?
CEO
Joined: 17 Nov 2007
Posts: 3589
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Followers: 544

Kudos [?]: 3550 [0], given: 360

### Show Tags

27 Nov 2009, 15:01
Expert's post
1
This post was
BOOKMARKED
1) each French book has to be separated at least by one English book, so we have following order:
*FE*FE*FE*FE*FE*FE*FE*FE*F* where * denotes 10 possible places for remained 11-8=3 English books

2) Now, let's count in how many ways we can place remained English books:

$$N = C^{10}_3+P^{10}_2+C^{10}_1 = \frac{10*9*8}{3*2} + 10*9 + 10 = 120 + 90 + 10 = 220$$

where

$$C^{10}_3$$ - all 3 books at distinct places.
$$P^{10}_2$$ - 2 books together and remained book at distinct place (order is important).
$$C^{10}_1$$ - all 3 books together.

maybe there is a better solution
_________________

HOT! GMAT TOOLKIT 2 (iOS) / GMAT TOOLKIT (Android) - The OFFICIAL GMAT CLUB PREP APP, a must-have app especially if you aim at 700+ | PrepGame

CEO
Joined: 17 Nov 2007
Posts: 3589
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Followers: 544

Kudos [?]: 3550 [1] , given: 360

### Show Tags

27 Nov 2009, 15:08
1
KUDOS
Expert's post
By the way, it is a good problem of 700+ level
+1
_________________

HOT! GMAT TOOLKIT 2 (iOS) / GMAT TOOLKIT (Android) - The OFFICIAL GMAT CLUB PREP APP, a must-have app especially if you aim at 700+ | PrepGame

Math Expert
Joined: 02 Sep 2009
Posts: 36520
Followers: 7067

Kudos [?]: 92926 [17] , given: 10528

### Show Tags

27 Nov 2009, 15:19
17
KUDOS
Expert's post
3
This post was
BOOKMARKED
I would offer different solution.

We have 11 English and 9 French books, no French books should be adjacent.

Imagine 11 English books in a row and empty slots like below:

*E*E*E*E*E*E*E*E*E*E*E*

Now if 9 French books would be placed in 12 empty slots, all French books will be separated by English books.

So we can "choose" 9 empty slots from 12 available for French books, which is 12C9=220.
_________________
CEO
Joined: 17 Nov 2007
Posts: 3589
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Followers: 544

Kudos [?]: 3550 [1] , given: 360

### Show Tags

27 Nov 2009, 15:32
1
KUDOS
Expert's post
I knew that there is a faster way

+1
_________________

HOT! GMAT TOOLKIT 2 (iOS) / GMAT TOOLKIT (Android) - The OFFICIAL GMAT CLUB PREP APP, a must-have app especially if you aim at 700+ | PrepGame

Intern
Joined: 27 Nov 2009
Posts: 2
Followers: 0

Kudos [?]: 4 [0], given: 2

### Show Tags

27 Nov 2009, 16:45
Bunuel, I wish I could adopt your way to look at the problem. Sometimes, it's an easy one lost in translation.
Walker, though your approach is different, but it's pretty interesting.
Thanks again guys, appreciate your help here.
Senior Manager
Joined: 25 Jun 2009
Posts: 293
Followers: 1

Kudos [?]: 153 [0], given: 4

### Show Tags

27 Nov 2009, 17:07
Wow, that was a faster way. Great explanation.
Intern
Joined: 16 Nov 2009
Posts: 5
Followers: 1

Kudos [?]: 2 [0], given: 0

### Show Tags

28 Nov 2009, 21:23
I am not very clear guys. Buenel, in your solution you have only considered the different ways that the 9 french books can be placed in 12 position. However, even the English books can be placed in their respective slots in more than one way. i.e. let the English books be 1e, 2e, 3e etc.
Now different placement of these english books can yield more possible combinations.

F 1e F 2e F 3e or
F 3e F 1e F 2e or
F 2e F 1e F 3e

Hope I am clear in expressing my doubt
Senior Manager
Joined: 25 Jun 2009
Posts: 293
Followers: 1

Kudos [?]: 153 [0], given: 4

### Show Tags

29 Nov 2009, 11:48
You do bring up a good point. I always have trouble imaging how to do these problems.
Intern
Joined: 28 Sep 2009
Posts: 37
Followers: 0

Kudos [?]: 2 [0], given: 2

### Show Tags

29 Nov 2009, 13:23
It is true that English books may have different positions but that's not what the question is asking.
It's only a matter of placing 9 books in 12 slots.
Math Expert
Joined: 02 Sep 2009
Posts: 36520
Followers: 7067

Kudos [?]: 92926 [7] , given: 10528

### Show Tags

29 Nov 2009, 13:37
7
KUDOS
Expert's post
4
This post was
BOOKMARKED
oracle wrote:
I am not very clear guys. Buenel, in your solution you have only considered the different ways that the 9 french books can be placed in 12 position. However, even the English books can be placed in their respective slots in more than one way. i.e. let the English books be 1e, 2e, 3e etc.
Now different placement of these english books can yield more possible combinations.

F 1e F 2e F 3e or
F 3e F 1e F 2e or
F 2e F 1e F 3e

Hope I am clear in expressing my doubt

Think I understand your point. You are saying that along with arrangements with no French books being adjacent, English and French books themselves could be arranged in different ways. But I don't think that this is the case. Though it's quite ambiguous question in a sense. Basically when GMAT wants us to consider some items as distinct it specifies this OR it's quite obvious. In original question we don't know whether these books are distinct or not: maybe all French and English books are the same, maybe not, we don't know that.

If the question were: how can we arrange 11 boys and 9 girls so that no girls are together, then the answer would be 12C9*11!*9!. As it's obvious that they are all different.

If the question were: how can we arrange 11 A-s and 9 B-s so that no B-s are together, then the answer would be 12C9. As it's obvious that A-s and B-s are the same.

Hope it's clear.
_________________
Senior Manager
Joined: 21 Jul 2009
Posts: 366
Schools: LBS, INSEAD, IMD, ISB - Anything with just 1 yr program.
Followers: 18

Kudos [?]: 163 [0], given: 22

### Show Tags

29 Nov 2009, 14:11
11 english books can be arranged in 11 slots (say) in 11! ways.
There will be 10 empty spaces between adjacent english books and another 2 empty spaces at either ends into which the french books can be placed such that no two french books are adjacent to one another. This is done in 12C9 ways.

Total number of ways should therefore be 12C9 * 11!.
_________________

I am AWESOME and it's gonna be LEGENDARY!!!

Math Expert
Joined: 02 Sep 2009
Posts: 36520
Followers: 7067

Kudos [?]: 92926 [6] , given: 10528

### Show Tags

29 Nov 2009, 14:56
6
KUDOS
Expert's post
2
This post was
BOOKMARKED
BarneyStinson wrote:
11 english books can be arranged in 11 slots (say) in 11! ways.
There will be 10 empty spaces between adjacent english books and another 2 empty spaces at either ends into which the french books can be placed such that no two french books are adjacent to one another. This is done in 12C9 ways.

Total number of ways should therefore be 12C9 * 11!.

Not so.

Let's say we have A1, A2, B1, B2 (meaning that A-s and B-s are distinct). We want to arrange them so that no B-s are adjacent:

*A1*A2* and we can place B1 and B2 in 3 empty slots. It can be done in 3C2 # of ways. BUT A1 and A2 can be arranged like *A1*A2* OR *A2*A1*, plus B1 and B2 can be arranged as B1B2 or B2B1.

Total # of ways 3C2*2!*2!=12.

Still if not convinced:
B1,A1,B2,A2
B1,A2,B2,A1
B2,A1,B1,A2
B2,A2,B1,A1

A1,B1,A2,B2
A2,B1,A1,B2
A1,B2,A2,B1
A2,B2,A1,B1,

B1,A1,A2,B2
B1,A2,A1,B2
B2,A1,A2,B1
B2,A2,A1,B1

BUT again this is the case when we have DISTINCT items. So, if we were told that all French book are different and all English books are different, then the answer would be 12C9*11!*9!.

In our original question we are not told that French books are different and are not told that English books are different. So # of ways would be 12C9.

Let's consider the easier example: # of ways to arrange two A-s and 2 B-s so that no B-s are adjacent: 3C2=3.

*A*A*

BABA
ABAB
BAAB

Hope it helps.
_________________
Intern
Joined: 16 Nov 2009
Posts: 5
Followers: 1

Kudos [?]: 2 [0], given: 0

### Show Tags

06 Dec 2009, 02:07
Thanks Buenel. Ya, It helps, here I was confused because it does not mention whether we should consider the English Books and the French books to be distinct, or as you said, like any A's and B's, which reduces the total number of possible arrangements.
Senior Manager
Joined: 25 Jun 2009
Posts: 293
Followers: 1

Kudos [?]: 153 [0], given: 4

### Show Tags

06 Dec 2009, 16:43
It seems possible that this question is somewhat unclear. What is the source of this question?
Manager
Joined: 22 Jul 2009
Posts: 201
Location: Manchester UK
Followers: 2

Kudos [?]: 384 [0], given: 6

### Show Tags

17 Dec 2009, 08:05
@Bunuel u really offer great solutions...thanks once again.
Intern
Joined: 03 Sep 2010
Posts: 16
Followers: 2

Kudos [?]: 9 [0], given: 106

### Show Tags

05 Oct 2010, 10:23
@bunuel - Just WOW!

I have never had the clearer picture of combination before .
Manager
Joined: 23 Sep 2013
Posts: 108
Concentration: Strategy, Marketing
WE: Engineering (Computer Software)
Followers: 2

Kudos [?]: 3 [0], given: 78

Re: In how many ways can 11 books on English and 9 books on [#permalink]

### Show Tags

17 Aug 2014, 22:35
Hi Bunuel !!

In the question it is mentioned that - ' 11 books on English and 9 books on French be placed in a row '.

As per the question since it says 11 books on English and 9 books on , it is implicitly saying that these books of French and English are of different subjects, therfore are distinct. I doubt if we should consider these books as similar.

So the answer should be: 12P9.11!

Please correct me if there is a gap in my understanding.
Re: In how many ways can 11 books on English and 9 books on   [#permalink] 17 Aug 2014, 22:35
Similar topics Replies Last post
Similar
Topics:
3 There are 4 identical pens and 7 identical books. In how many ways can 3 13 Mar 2016, 09:41
In how many ways can the crew 2 27 Oct 2010, 03:18
1 In how many ways can 4 2 27 Oct 2010, 03:05
50 In how many different ways can a group of 9 people be divide 14 26 Sep 2010, 08:47
14 In how many different ways can a group of 9 people be 12 29 Oct 2009, 04:30
Display posts from previous: Sort by

# In how many ways can 11 books on English and 9 books on

 Powered by phpBB © phpBB Group and phpBB SEO Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.