Last visit was: 19 Nov 2025, 11:04 It is currently 19 Nov 2025, 11:04
Home
GMAT
Messages
Tests
Schools
Events
Rewards
Chat
My Profile
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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
User avatar
Ravshonbek
User avatar
Joined: 09 Jul 2007
Last visit: 15 Jul 2008
Posts: 565
Own Kudos:
571
 [42]
Location: London
Posts: 565
Kudos: 571
 [42]
In how many different ways can 4 physics, 2 math and 3 chemistry books Updated on: 15 Mar 2019, 04:18
Originally posted by Ravshonbek on 11 Nov 2007, 04:37.
Last edited by Bunuel on 15 Mar 2019, 04:18, edited 1 time in total.
Renamed the topic and edited the question.
3
Kudos
Add Kudos
39
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

25% (medium)

Question Stats:

78% (01:44) correct 22% (02:12) wrong based on 1132 sessions

History

Date
Time
Result
Not Attempted Yet
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
ShowHide Answer
Official Answer
B
Most Helpful Reply
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 19 Nov 2025
Posts: 105,390
Own Kudos:
778,310
 [13]
Given Kudos: 99,977
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 105,390
Kudos: 778,310
 [13]
In how many different ways can 4 physics, 2 math and 3 chemistry books 05 May 2010, 01:54
9
Kudos
Add Kudos
4
Bookmarks
Bookmark this Post
bibha
hey,
Looks like the question is too easy for further explanation. However, i could not understand how we got that answer.
Pleaseeee reply.
Show more

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.
General Discussion
avatar
srivas
avatar
Joined: 27 Oct 2008
Last visit: 28 Sep 2009
Posts: 95
Own Kudos:
310
 [4]
Given Kudos: 3
Posts: 95
Kudos: 310
 [4]
In how many different ways can 4 physics, 2 math and 3 chemistry books 28 Sep 2009, 10:41
3
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
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
User avatar
bibha
User avatar
Joined: 14 Apr 2010
Last visit: 06 Jan 2011
Posts: 97
Own Kudos:
1,176
 [1]
Given Kudos: 1
Posts: 97
Kudos: 1,176
 [1]
In how many different ways can 4 physics, 2 math and 3 chemistry books 05 May 2010, 00:18
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
hey,
Looks like the question is too easy for further explanation. However, i could not understand how we got that answer.
Pleaseeee reply.
avatar
viveksingh222
avatar
Joined: 19 Nov 2012
Last visit: 24 Feb 2013
Posts: 1
Given Kudos: 7
Posts: 1
Kudos: 0
In how many different ways can 4 physics, 2 math and 3 chemistry books 06 Feb 2013, 16:15
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
bibha
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.
Show more


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.
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 19 Nov 2025
Posts: 105,390
Own Kudos:
778,310
 [4]
Given Kudos: 99,977
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 105,390
Kudos: 778,310
 [4]
In how many different ways can 4 physics, 2 math and 3 chemistry books 07 Feb 2013, 00:46
3
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
viveksingh222
Bunuel
bibha
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.
Show more

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.
User avatar
solitaryreaper
User avatar
Joined: 23 Sep 2013
Last visit: 21 Feb 2023
Posts: 119
Own Kudos:
221
Given Kudos: 95
Concentration: Strategy, Marketing
Schools: Boston U '20 (WL)
WE:Engineering (Computer Software)
Products:
My Reviews
Schools: Boston U '20 (WL)
Posts: 119
Kudos: 221
In how many different ways can 4 physics, 2 math and 3 chemistry books 18 Aug 2014, 00:59
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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 !!!!
User avatar
PerfectScores
User avatar
Joined: 20 Dec 2013
Last visit: 19 Mar 2025
Posts: 104
Own Kudos:
274
Given Kudos: 1
Expert
Expert reply
Posts: 104
Kudos: 274
In how many different ways can 4 physics, 2 math and 3 chemistry books 18 Aug 2014, 01:19
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Ravshonbek
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
Show more


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

The last 3! came for the number of ways Physics, Math and Chemistry are arranged.
User avatar
tushain
User avatar
Joined: 17 Mar 2014
Last visit: 14 Apr 2015
Posts: 30
Own Kudos:
228
Given Kudos: 34
Location: India
Concentration: Strategy, Marketing
Schools: Kenan-Flagler '17 (A)
GMAT 1: 760 Q50 V44
WE:Medicine and Health (Healthcare/Pharmaceuticals)
Schools: Kenan-Flagler '17 (A)
GMAT 1: 760 Q50 V44
Posts: 30
Kudos: 228
In how many different ways can 4 physics, 2 math and 3 chemistry books 28 Aug 2014, 22:00
Kudos
Add Kudos
Bookmarks
Bookmark this Post
solitaryreaper
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 !!!!
Show more

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!
avatar
bazc
avatar
Joined: 27 Aug 2014
Last visit: 25 Jul 2016
Posts: 26
Own Kudos:
156
Given Kudos: 25
GMAT Date: 09-27-2014
Posts: 26
Kudos: 156
In how many different ways can 4 physics, 2 math and 3 chemistry books 28 Aug 2014, 22:24
Kudos
Add Kudos
Bookmarks
Bookmark this Post
tushain
solitaryreaper
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!
Show more

Because then it would be unsolvable. GMAT questions ideally state this explicitly.
avatar
OptimusPrepJanielle
avatar
Joined: 06 Nov 2014
Last visit: 08 Sep 2017
Posts: 1,779
Own Kudos:
1,483
Given Kudos: 23
Expert
Expert reply
Posts: 1,779
Kudos: 1,483
In how many different ways can 4 physics, 2 math and 3 chemistry books 06 Jul 2016, 08:08
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Ravshonbek
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
Show more

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
User avatar
Senthil1981
User avatar
Joined: 23 Apr 2015
Last visit: 14 Oct 2021
Posts: 225
Own Kudos:
602
Given Kudos: 36
Location: United States
Concentration: General Management, International Business
Schools: Booth PT '19 Ross Weekend"19
WE:Engineering (Consulting)
Schools: Booth PT '19 Ross Weekend"19
Posts: 225
Kudos: 602
In how many different ways can 4 physics, 2 math and 3 chemistry books 24 Aug 2016, 11:32
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Ravshonbek
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
Show more


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!
avatar
HappyQuakka
avatar
Joined: 10 Aug 2017
Last visit: 22 Nov 2017
Posts: 16
Own Kudos:
12
Given Kudos: 122
GMAT 1: 720 Q48 V41
GMAT 1: 720 Q48 V41
Posts: 16
Kudos: 12
In how many different ways can 4 physics, 2 math and 3 chemistry books 15 Sep 2017, 02:56
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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!!
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 19 Nov 2025
Posts: 105,390
Own Kudos:
778,310
Given Kudos: 99,977
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 105,390
Kudos: 778,310
In how many different ways can 4 physics, 2 math and 3 chemistry books 15 Sep 2017, 03:10
Kudos
Add Kudos
Bookmarks
Bookmark this Post
HappyQuakka
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!!
Show more

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.
User avatar
JeffTargetTestPrep
User avatar
Target Test Prep Representative
Joined: 04 Mar 2011
Last visit: 05 Jan 2024
Posts: 2,977
Own Kudos:
8,390
Given Kudos: 1,646
Status:Head GMAT Instructor
Affiliations: Target Test Prep
Expert
Expert reply
Posts: 2,977
Kudos: 8,390
In how many different ways can 4 physics, 2 math and 3 chemistry books 16 Sep 2017, 07:32
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Ravshonbek
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
Show more

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
User avatar
lnyngayan
User avatar
Joined: 09 Mar 2023
Last visit: 13 Oct 2024
Posts: 27
Own Kudos:
1
Given Kudos: 239
Posts: 27
Kudos: 1
In how many different ways can 4 physics, 2 math and 3 chemistry books 03 Sep 2024, 10:20
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel

bibha
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.
Show more
­Hello! Wonder how to calculate 3!*4!*2!*3! this quickly?
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 19 Nov 2025
Posts: 105,390
Own Kudos:
778,310
 [1]
Given Kudos: 99,977
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 105,390
Kudos: 778,310
 [1]
In how many different ways can 4 physics, 2 math and 3 chemistry books 03 Sep 2024, 10:30
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
lnyngayan

Bunuel

bibha
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.
­Hello! Wonder how to calculate 3!*4!*2!*3! this quickly?
Show more

­3!*4!*2!*3! = 6*24*2*6 = something with the units digit of 8.

Or just calculate 6*24*2*6 = 72*24.
Moderators:
Bunuel
Math Expert
105390 posts
Krunaal
Tuck School Moderator
805 posts