In how many different ways can 4 physics, 2 math and 3 : GMAT Problem Solving (PS)
Check GMAT Club App Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 09 Dec 2016, 15:10

### 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 different ways can 4 physics, 2 math and 3

Author Message
TAGS:

### Hide Tags

VP
Joined: 09 Jul 2007
Posts: 1104
Location: London
Followers: 6

Kudos [?]: 101 [0], given: 0

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

### Show Tags

11 Nov 2007, 03:37
5
This post was
BOOKMARKED
00:00

Difficulty:

15% (low)

Question Stats:

80% (02:12) correct 20% (01:51) wrong based on 440 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
Manager
Joined: 27 Oct 2008
Posts: 185
Followers: 2

Kudos [?]: 140 [2] , given: 3

### Show Tags

28 Sep 2009, 09:41
2
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
Manager
Joined: 14 Apr 2010
Posts: 230
Followers: 2

Kudos [?]: 147 [0], given: 1

### Show Tags

04 May 2010, 23:18
hey,
Looks like the question is too easy for further explanation. However, i could not understand how we got that answer.
Math Expert
Joined: 02 Sep 2009
Posts: 35932
Followers: 6860

Kudos [?]: 90098 [5] , given: 10413

### Show Tags

05 May 2010, 00:54
5
KUDOS
Expert's post
1
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.

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!.

_________________
Intern
Joined: 19 Nov 2012
Posts: 2
Followers: 0

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

### Show Tags

06 Feb 2013, 15:15
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.

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!.

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.
Math Expert
Joined: 02 Sep 2009
Posts: 35932
Followers: 6860

Kudos [?]: 90098 [1] , given: 10413

### Show Tags

06 Feb 2013, 23:46
1
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.

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!.

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.
_________________
Manager
Joined: 23 Sep 2013
Posts: 106
Concentration: Strategy, Marketing
WE: Engineering (Computer Software)
Followers: 2

Kudos [?]: 0 [0], given: 77

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

### Show Tags

17 Aug 2014, 23:59
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

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.

Manager
Joined: 20 Dec 2013
Posts: 125
Followers: 9

Kudos [?]: 92 [0], given: 1

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

### Show Tags

18 Aug 2014, 00:19
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.
Current Student
Joined: 17 Mar 2014
Posts: 44
Location: India
Concentration: Strategy, Marketing
GMAT 1: 760 Q50 V44
WE: Medicine and Health (Health Care)
Followers: 1

Kudos [?]: 16 [0], given: 34

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

### Show Tags

28 Aug 2014, 21:00
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

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.

Thanks!
Exact same query? When do we have to consider the books different and when same , if it is not explicitly stated?
Intern
Joined: 27 Aug 2014
Posts: 30
GMAT Date: 09-27-2014
Followers: 1

Kudos [?]: 10 [0], given: 25

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

### Show Tags

28 Aug 2014, 21:24
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

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.

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

Because then it would be unsolvable. GMAT questions ideally state this explicitly.
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 12904
Followers: 562

Kudos [?]: 158 [0], given: 0

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

### Show Tags

14 Nov 2015, 05:34
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.
_________________
Optimus Prep Instructor
Joined: 06 Nov 2014
Posts: 1738
Followers: 50

Kudos [?]: 378 [0], given: 21

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

### Show Tags

06 Jul 2016, 07:08
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

Senior Manager
Joined: 23 Apr 2015
Posts: 339
Location: United States
WE: Engineering (Consulting)
Followers: 5

Kudos [?]: 63 [0], given: 36

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

### Show Tags

24 Aug 2016, 10:32
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!
Re: In how many different ways can 4 physics, 2 math and 3   [#permalink] 24 Aug 2016, 10:32
Similar topics Replies Last post
Similar
Topics:
3 In how many ways can we put 4 different balls in 3 different boxes whe 3 28 Sep 2016, 09:40
41 In how many ways can 5 different marbles be distributed in 4 19 27 Apr 2014, 23:59
10 In how many different ways can 3 identical green shirts and 15 25 Nov 2010, 17:54
16 In how many different ways can 4 ladies and 4 gentlemen be 7 04 Oct 2010, 05:40
8 In how many ways 5 different balls can be arranged in to 3 7 07 Aug 2010, 05:10
Display posts from previous: Sort by