It is currently 20 Sep 2017, 17:00

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

In how many different ways can 4 physics, 2 math and 3

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

1 KUDOS received
VP
VP
User avatar
Joined: 09 Jul 2007
Posts: 1098

Kudos [?]: 139 [1], given: 0

Location: London
In how many different ways can 4 physics, 2 math and 3 [#permalink]

Show Tags

New post 11 Nov 2007, 04:37
1
This post received
KUDOS
9
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

81% (01:08) correct 19% (01:58) wrong based on 459 sessions

HideShow timer Statistics

In how many different ways can 4 physics, 2 math and 3 chemistry books be arranged in a row so that all books of the same branch are together?

A. 1242
B. 1728
C. 1484
D. 1734
E. 1726
[Reveal] Spoiler: OA

Kudos [?]: 139 [1], given: 0

2 KUDOS received
Manager
Manager
avatar
Joined: 27 Oct 2008
Posts: 185

Kudos [?]: 161 [2], given: 3

Re: perm [#permalink]

Show Tags

New post 28 Sep 2009, 10:41
2
This post received
KUDOS
1
This post was
BOOKMARKED
In how many different ways can 4 physics, 2 math and 3 chemistry books be arranged in a row so that all books of the same branch are together?

A. 1242
B. 1728
C. 1484
D. 1734
E. 1726

Soln:
= 3! * 4! * 2! * 3!
= 1728

Ans is B

Kudos [?]: 161 [2], given: 3

Manager
Manager
avatar
Joined: 14 Apr 2010
Posts: 219

Kudos [?]: 222 [0], given: 1

Re: perm [#permalink]

Show Tags

New post 05 May 2010, 00:18
hey,
Looks like the question is too easy for further explanation. However, i could not understand how we got that answer.
Pleaseeee reply.

Kudos [?]: 222 [0], given: 1

Expert Post
5 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41640

Kudos [?]: 124200 [5], given: 12075

Re: perm [#permalink]

Show Tags

New post 05 May 2010, 01:54
5
This post received
KUDOS
Expert's post
2
This post was
BOOKMARKED
bibha wrote:
hey,
Looks like the question is too easy for further explanation. However, i could not understand how we got that answer.
Pleaseeee reply.


In how many different ways can 4 physics, 2 math and 3 chemistry books be arranged in a row so that all books of the same branch are together?

A. 1242
B. 1728
C. 1484
D. 1734
E. 1726

There are three branches, three units of books: {physics}{math}{chemistry} - aranging branches 3!;

Arranging the books within the branches:
physics - 4!;
math - 2!;
chemistry - 3!;

Total: 3!*4!*2!*3!.

Answer: B.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 124200 [5], given: 12075

Intern
Intern
avatar
Joined: 19 Nov 2012
Posts: 2

Kudos [?]: [0], given: 7

Re: perm [#permalink]

Show Tags

New post 06 Feb 2013, 16:15
Bunuel wrote:
bibha wrote:
hey,
Looks like the question is too easy for further explanation. However, i could not understand how we got that answer.
Pleaseeee reply.


In how many different ways can 4 physics, 2 math and 3 chemistry books be arranged in a row so that all books of the same branch are together?

A. 1242
B. 1728
C. 1484
D. 1734
E. 1726

There are three branches, three units of books: {physics}{math}{chemistry} - aranging branches 3!;

Arranging the books within the branches:
physics - 4!;
math - 2!;
chemistry - 3!;

Total: 3!*4!*2!*3!.

Answer: B.



Hi Bunuel,
I apologize for opening a very old post but had to ..
my doubt is if we are arranging 4 physics books then doesn't the arrangement will be 4!/4!, similarly math and chemistry..and over all arrangement should be just 3!..please explain where I am missing..
Thank you,
Vivek.

Kudos [?]: [0], given: 7

Expert Post
1 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41640

Kudos [?]: 124200 [1], given: 12075

Re: perm [#permalink]

Show Tags

New post 07 Feb 2013, 00:46
1
This post received
KUDOS
Expert's post
1
This post was
BOOKMARKED
viveksingh222 wrote:
Bunuel wrote:
bibha wrote:
hey,
Looks like the question is too easy for further explanation. However, i could not understand how we got that answer.
Pleaseeee reply.


In how many different ways can 4 physics, 2 math and 3 chemistry books be arranged in a row so that all books of the same branch are together?

A. 1242
B. 1728
C. 1484
D. 1734
E. 1726

There are three branches, three units of books: {physics}{math}{chemistry} - aranging branches 3!;

Arranging the books within the branches:
physics - 4!;
math - 2!;
chemistry - 3!;

Total: 3!*4!*2!*3!.

Answer: B.



Hi Bunuel,
I apologize for opening a very old post but had to ..
my doubt is if we are arranging 4 physics books then doesn't the arrangement will be 4!/4!, similarly math and chemistry..and over all arrangement should be just 3!..please explain where I am missing..
Thank you,
Vivek.


It would be so if we were told that books in each branch are identical. But that's not our case, for example, out of 2 math books one could be on algebra and another on arithmetic thus they can be arranged within math branch as {algebra}{arithmetic} or {arithmetic }{algebra}.

Hope it's clear.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 124200 [1], given: 12075

Manager
Manager
User avatar
Joined: 23 Sep 2013
Posts: 105

Kudos [?]: 26 [0], given: 80

Concentration: Strategy, Marketing
WE: Engineering (Computer Software)
Reviews Badge
Re: In how many different ways can 4 physics, 2 math and 3 [#permalink]

Show Tags

New post 18 Aug 2014, 00:59
Hi Bunuel !!

I am not sure why you have assumed that the books within one subject are actually different !
I believe the books can also be same , solution in that case should be 3!.

You have assumed the same in this problem :

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?

in-how-many-ways-can-11-books-on-english-and-9-books-on-87352.html#p1394032

Your solution was :
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.



I believe in both these questions we should consider the books to be different. But I am confused because of the two opposite approaches applied to 2 similar problems. Where should one draw the line.

Please have a look . Thanks in advance !!!!

Kudos [?]: 26 [0], given: 80

Manager
Manager
User avatar
Joined: 20 Dec 2013
Posts: 131

Kudos [?]: 103 [0], given: 1

Re: In how many different ways can 4 physics, 2 math and 3 [#permalink]

Show Tags

New post 18 Aug 2014, 01:19
Ravshonbek wrote:
In how many different ways can 4 physics, 2 math and 3 chemistry books be arranged in a row so that all books of the same branch are together?

A. 1242
B. 1728
C. 1484
D. 1734
E. 1726



4! x 2! x 3! x 3! = 1728

The last 3! came for the number of ways Physics, Math and Chemistry are arranged.
_________________

76000 Subscribers, 7 million minutes of learning delivered and 5.6 million video views

Perfect Scores
http://perfectscores.org
http://www.youtube.com/perfectscores

Kudos [?]: 103 [0], given: 1

Current Student
avatar
Joined: 17 Mar 2014
Posts: 40

Kudos [?]: 17 [0], given: 34

Location: India
Concentration: Strategy, Marketing
GMAT 1: 760 Q50 V44
WE: Medicine and Health (Health Care)
Re: In how many different ways can 4 physics, 2 math and 3 [#permalink]

Show Tags

New post 28 Aug 2014, 22:00
solitaryreaper wrote:
Hi Bunuel !!

I am not sure why you have assumed that the books within one subject are actually different !
I believe the books can also be same , solution in that case should be 3!.

You have assumed the same in this problem :

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?

in-how-many-ways-can-11-books-on-english-and-9-books-on-87352.html#p1394032

Your solution was :
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.



I believe in both these questions we should consider the books to be different. But I am confused because of the two opposite approaches applied to 2 similar problems. Where should one draw the line.

Please have a look . Thanks in advance !!!!


Thanks!
Exact same query? When do we have to consider the books different and when same , if it is not explicitly stated?
Experts please answer... TIA!

Kudos [?]: 17 [0], given: 34

Intern
Intern
avatar
Joined: 27 Aug 2014
Posts: 30

Kudos [?]: 21 [0], given: 25

GMAT Date: 09-27-2014
GMAT ToolKit User
Re: In how many different ways can 4 physics, 2 math and 3 [#permalink]

Show Tags

New post 28 Aug 2014, 22:24
tushain wrote:
solitaryreaper wrote:
Hi Bunuel !!

I am not sure why you have assumed that the books within one subject are actually different !
I believe the books can also be same , solution in that case should be 3!.

You have assumed the same in this problem :

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?

in-how-many-ways-can-11-books-on-english-and-9-books-on-87352.html#p1394032

Your solution was :
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.



I believe in both these questions we should consider the books to be different. But I am confused because of the two opposite approaches applied to 2 similar problems. Where should one draw the line.

Please have a look . Thanks in advance !!!!


Thanks!
Exact same query? When do we have to consider the books different and when same , if it is not explicitly stated?
Experts please answer... TIA!


Because then it would be unsolvable. GMAT questions ideally state this explicitly.

Kudos [?]: 21 [0], given: 25

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 17576

Kudos [?]: 270 [0], given: 0

Premium Member
Re: In how many different ways can 4 physics, 2 math and 3 [#permalink]

Show Tags

New post 14 Nov 2015, 06:34
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Kudos [?]: 270 [0], given: 0

Expert Post
Optimus Prep Instructor
User avatar
B
Joined: 06 Nov 2014
Posts: 1905

Kudos [?]: 515 [0], given: 23

In how many different ways can 4 physics, 2 math and 3 [#permalink]

Show Tags

New post 06 Jul 2016, 08:08
Ravshonbek wrote:
In how many different ways can 4 physics, 2 math and 3 chemistry books be arranged in a row so that all books of the same branch are together?

A. 1242
B. 1728
C. 1484
D. 1734
E. 1726


Total books: 4 Math, 3 English, 2 Analytical Ability
Assume the books of each subject to be a bundle
Hence we have 3 bundles of Math, English and Analytical Ability

Total ways to arranging 3 bundles = 3!
Books inside each bundle can also be arranged.

Total ways = 3!*4!*3!*2! = 6*24*6*2 = 36*48 = 1728
By paying attention to the options, we can reach the correct one without calculating
As the answer would be a number rending with the digit 8 and there is only one such number in the given options.

Correct Option: B
_________________

Janielle Williams

Customer Support

Special Offer: $80-100/hr. Online Private Tutoring
GMAT On Demand Course $299
Free Online Trial Hour

Kudos [?]: 515 [0], given: 23

Senior Manager
Senior Manager
avatar
Joined: 23 Apr 2015
Posts: 332

Kudos [?]: 99 [0], given: 36

Location: United States
Concentration: General Management, International Business
WE: Engineering (Consulting)
Re: In how many different ways can 4 physics, 2 math and 3 [#permalink]

Show Tags

New post 24 Aug 2016, 11:32
Ravshonbek wrote:
In how many different ways can 4 physics, 2 math and 3 chemistry books be arranged in a row so that all books of the same branch are together?

A. 1242
B. 1728
C. 1484
D. 1734
E. 1726



4 physics book can be arranged among themselves in 4! ways
Similarly, 3 chemistry and 2 math in 3! and 2! ways.

Now considering them as 3 groups, the 3 groups can be arranged in 3! ways.

so the total number of ways = 4! * 3! * 2! * 3!

Kudos [?]: 99 [0], given: 36

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 17576

Kudos [?]: 270 [0], given: 0

Premium Member
Re: In how many different ways can 4 physics, 2 math and 3 [#permalink]

Show Tags

New post 14 Sep 2017, 06:06
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Kudos [?]: 270 [0], given: 0

Intern
Intern
avatar
B
Joined: 10 Aug 2017
Posts: 15

Kudos [?]: 2 [0], given: 88

Re: In how many different ways can 4 physics, 2 math and 3 [#permalink]

Show Tags

New post 15 Sep 2017, 02:56
I am pretty sure this is a stupid question but here it goes:

Each category of books can be arranged the following number of ways.
physics 4!; math 2!; chemistry 3!;

there are three categories, so the number of ways which different categories can be arranged is 3!.
Now, here's my problem. Bunuel

I thought it would be (3!+4!+2!)*3!, because these are number of ways which the books of different categories are being arranged.

Why should they be multiplied?

Thank you!!

Kudos [?]: 2 [0], given: 88

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41640

Kudos [?]: 124200 [0], given: 12075

Re: In how many different ways can 4 physics, 2 math and 3 [#permalink]

Show Tags

New post 15 Sep 2017, 03:10
HappyQuakka wrote:
I am pretty sure this is a stupid question but here it goes:

Each category of books can be arranged the following number of ways.
physics 4!; math 2!; chemistry 3!;

there are three categories, so the number of ways which different categories can be arranged is 3!.
Now, here's my problem. Bunuel

I thought it would be (3!+4!+2!)*3!, because these are number of ways which the books of different categories are being arranged.

Why should they be multiplied?

Thank you!!


Say the order is {physics: 1, 2, 3, 4}{math: 1, 2}{chemistry: 1, 2, 3}

For two ordering of say {math: 1, 2}: {1, 2} and {2, 1} we'll have:
{physics: 1, 2, 3, 4}{math: 1, 2}{chemistry: 1, 2, 3}
{physics: 1, 2, 3, 4}{math: 2, 1}{chemistry: 1, 2, 3}

Similarly for all 3! orderings of {chemistry: 1, 2, 3} we'll have 6 times as many for each above 2!*3! and for 4! orderings of {physics: 1, 2, 3, 4} we'll have 24 as many as previous number, so 2!*3!*4!.

More generally, we multiply because of FUNDAMENTAL PRINCIPLE OF COUNTING, which states if an operation can be performed in ‘m’ ways and when it has been performed in any of these ways, a second operation that can be performed in ‘n’ ways then these two operations can be performed one after the other in ‘m*n’ ways.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 124200 [0], given: 12075

Expert Post
Target Test Prep Representative
User avatar
S
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 1414

Kudos [?]: 756 [0], given: 5

Re: In how many different ways can 4 physics, 2 math and 3 [#permalink]

Show Tags

New post 16 Sep 2017, 07:32
Ravshonbek wrote:
In how many different ways can 4 physics, 2 math and 3 chemistry books be arranged in a row so that all books of the same branch are together?

A. 1242
B. 1728
C. 1484
D. 1734
E. 1726


We can illustrate the arrangement as follows:

[P-P-P-P] [M-M] [C-C-C]

So, the 3 groups of books can be arranged in 3! = 6 ways. Furthermore, the physics books can be arranged in 4! = 24 ways, the math books in 2! = 2 ways, and the chemistry books in 3! = 6 ways.

Thus, the total number of ways to arrange the books is 6 x 24 x 2 x 6 = 1728 ways.

Answer: B
_________________

Jeffery Miller
Head of GMAT Instruction

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Kudos [?]: 756 [0], given: 5

Re: In how many different ways can 4 physics, 2 math and 3   [#permalink] 16 Sep 2017, 07:32
    Similar topics Author Replies Last post
Similar
Topics:
21 EXPERTS_POSTS_IN_THIS_TOPIC How many ways can 5 different colored marbles be placed in 3 praffulpatel 7 18 Aug 2016, 23:47
45 EXPERTS_POSTS_IN_THIS_TOPIC In how many ways can 5 different marbles be distributed in 4 tusharGupta1 20 10 Sep 2017, 08:54
1 EXPERTS_POSTS_IN_THIS_TOPIC In how many ways can 4 different portraits be mounted on 4 of the four GMATinsight 1 17 Feb 2017, 02:16
18 EXPERTS_POSTS_IN_THIS_TOPIC In how many different ways can 4 ladies and 4 gentlemen be eladshush 7 29 Aug 2016, 02:17
10 In how many ways can we put 4 different balls in 3 different boxes whe geetgmat 4 12 Mar 2017, 09:24
Display posts from previous: Sort by

In how many different ways can 4 physics, 2 math and 3

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

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®.