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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.