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

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

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New post 26 Mar 2017, 07:01
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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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Re: A book store has received 8 different books, of which 3/8 are novels,  [#permalink]

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New post 26 Mar 2017, 09:12
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Answer: [E]

novels = 3
study guides = 2
textbooks = 3

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

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New post 24 May 2017, 23:28
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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
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Re: A book store has received 8 different books, of which 3/8 are novels,  [#permalink]

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New post 24 May 2017, 23:39
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
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Re: A book store has received 8 different books, of which 3/8 are novels,  [#permalink]

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New post 31 May 2017, 18:57
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.

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

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New post 19 Sep 2018, 13:41
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Re: A book store has received 8 different books, of which 3/8 are novels,   [#permalink] 19 Sep 2018, 13:41
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