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# A book store has received 8 different books, of which 3/8 are novels,

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Math Expert
Joined: 02 Sep 2009
Posts: 64322
A book store has received 8 different books, of which 3/8 are novels,  [#permalink]

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26 Mar 2017, 06:01
11
00:00

Difficulty:

45% (medium)

Question Stats:

62% (01:52) correct 38% (02:05) wrong based on 155 sessions

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A book store has received 8 different books, of which 3/8 are novels, 25% are study guides and remaining are textbooks. If all books must be placed on one shelf displaying new items and if books in the same category have to be shelved next to each other, how many different arrangements of books are possible?

A. 18
B. 36
C. 72
D. 216
E. 432

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Manager
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Posts: 56
Location: India
GMAT 1: 680 Q49 V34
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Re: A book store has received 8 different books, of which 3/8 are novels,  [#permalink]

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26 Mar 2017, 08:12
2

novels = 3
study guides = 2
textbooks = 3

total ways = 3! * 3! * 2! * 3! = 432 [arrangement between categories (3!) * individual arrangements ]
Intern
Joined: 22 Mar 2017
Posts: 15
Re: A book store has received 8 different books, of which 3/8 are novels,  [#permalink]

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24 May 2017, 22:28
1
There are 3 Novels, 2 Study Guides, and 3 Text Books.

The question specifies that books in the same category have to be shelved next to each other. This gives us 3! in addition to all of the different arrangements within each category.

Thus, Novel arrangements * Study Guide arrangements * Text Book arrangements * Category arrangements on the shelf = 3! * 2! * 3! * 3! = 432
Manager
Joined: 23 May 2017
Posts: 225
Concentration: Finance, Accounting
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Re: A book store has received 8 different books, of which 3/8 are novels,  [#permalink]

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24 May 2017, 22:39
1
Total Books : 8
Novels = 3/8 of 8 = 3
Study Guides = 25% = 1/4 of 8 = 2
Text books = 8 - 5 = 3

Arranging Novels , Study Guides and Text Books : NST ( 3! ways)
=> N itself has 3 different books which can be arranged in 3! ways
=> S has 2 different books which can be arranged in 2! ways
=> Text books can be arranged in 3! ways

so total arrangement possible : 3! * 3! * 2! * 3! = 6 * 6 * 2* 6 = 432
Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2799
Re: A book store has received 8 different books, of which 3/8 are novels,  [#permalink]

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31 May 2017, 17:57
Bunuel wrote:
A book store has received 8 different books, of which 3/8 are novels, 25% are study guides and remaining are textbooks. If all books must be placed on one shelf displaying new items and if books in the same category have to be shelved next to each other, how many different arrangements of books are possible?

A. 18
B. 36
C. 72
D. 216
E. 432

The store has 3/8 x 8 = 3 novels, 1/4 x 8 = 2 study guides, and 3 textbooks.

We can let n = a novel, s = study guide, and t = textbook.

Since the each category of book has to be next to each other, we have:

[n(1)-n(2)-n(3)] [s(1)-s(2)] [t(1)-t(2)-t(3)]

We have 3 categories of books (novels, study guides, and textbooks), and so those categories of books can be arranged in 3! = 6 ways.

Now, let’s arrange the books within each category. The novels can be arranged in 3! = 6 ways, the study guides in 2! = 2 ways, and the textbooks in 3! = 6 ways.

Thus, the total number of ways to arrange the books is 6 x 6 x 2 x 6 = 432 ways.

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Re: A book store has received 8 different books, of which 3/8 are novels,  [#permalink]

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07 Apr 2020, 14:25
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).

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Re: A book store has received 8 different books, of which 3/8 are novels,   [#permalink] 07 Apr 2020, 14:25