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

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VP
Joined: 09 Jul 2007
Posts: 1054
Location: London
In how many different ways can 4 physics, 2 math and 3  [#permalink]

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11 Nov 2007, 03:37
2
10
00:00

Difficulty:

15% (low)

Question Stats:

76% (01:40) correct 24% (02:12) wrong based on 601 sessions

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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
Math Expert
Joined: 02 Sep 2009
Posts: 52231

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05 May 2010, 00:54
5
2
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!.

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##### General Discussion
Manager
Joined: 27 Oct 2008
Posts: 177

### Show Tags

28 Sep 2009, 09:41
3
1
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: 179

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04 May 2010, 23:18
1
hey,
Looks like the question is too easy for further explanation. However, i could not understand how we got that answer.
Intern
Joined: 19 Nov 2012
Posts: 1

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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: 52231

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06 Feb 2013, 23:46
1
1
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.
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Joined: 23 Sep 2013
Posts: 134
Concentration: Strategy, Marketing
WE: Engineering (Computer Software)
Re: In how many different ways can 4 physics, 2 math and 3  [#permalink]

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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: 122
Re: In how many different ways can 4 physics, 2 math and 3  [#permalink]

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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.
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Intern
Joined: 17 Mar 2014
Posts: 35
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]

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

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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.
SVP
Joined: 06 Nov 2014
Posts: 1877
In how many different ways can 4 physics, 2 math and 3  [#permalink]

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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
Senior Manager
Joined: 23 Apr 2015
Posts: 302
Location: United States
WE: Engineering (Consulting)
Re: In how many different ways can 4 physics, 2 math and 3  [#permalink]

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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!
Intern
Joined: 10 Aug 2017
Posts: 17
GMAT 1: 720 Q48 V41
Re: In how many different ways can 4 physics, 2 math and 3  [#permalink]

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15 Sep 2017, 01:56
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!!
Math Expert
Joined: 02 Sep 2009
Posts: 52231
Re: In how many different ways can 4 physics, 2 math and 3  [#permalink]

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15 Sep 2017, 02:10
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.
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Re: In how many different ways can 4 physics, 2 math and 3  [#permalink]

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16 Sep 2017, 06:32
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.

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

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16 Jan 2018, 10:55
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

the question did not make clear that all physics, math, and chemistry books are different, but looking at the answer choices, we can see that the answer is not 3!

easy question, but little ambiguous

thanks
Re: In how many different ways can 4 physics, 2 math and 3 &nbs [#permalink] 16 Jan 2018, 10:55
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