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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.
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}.
Re: In how many different ways can 4 physics, 2 math and 3 [#permalink]
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?
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.
Re: In how many different ways can 4 physics, 2 math and 3 [#permalink]
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?
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!
Re: In how many different ways can 4 physics, 2 math and 3 [#permalink]
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?
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.
Re: In how many different ways can 4 physics, 2 math and 3 [#permalink]
14 Nov 2015, 05:34
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