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In how many different ways can 3 fiction books and 3

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In how many different ways can 3 fiction books and 3

by VJesus12 » Mon Jun 17, 2019 2:58 am

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In how many different ways can 3 fiction books and 3 non-fiction books be arranged in a row of 6 books on a shelf such that the fiction books are not separated, and the non-fiction books are not separated?

A. 24
B. 36
C. 72
D. 144
E. 288

[spoiler]OA=C[/spoiler]

Source: Magoosh
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by GMATGuruNY » Mon Jun 17, 2019 3:30 am
VJesus12 wrote:In how many different ways can 3 fiction books and 3 non-fiction books be arranged in a row of 6 books on a shelf such that the fiction books are not separated, and the non-fiction books are not separated?

A. 24
B. 36
C. 72
D. 144
E. 288
Case 1: The 3 fiction books appear to the left of the 3 nonfiction books
Number of ways to arrange the 3 fiction books = 3! = 6
Number of ways to arrange the 3 nonfiction books = 3! = 6
To combine these options, we multiply:
6*6 = 36

Case 2: The 3 nonfiction books appear to the left of the 3 fiction books
As in Case 1, the number of possible arrangements = 36.

Total ways = Case 1 + Case 2 = 36 + 36 = 72.

The correct answer is C.
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by Scott@TargetTestPrep » Wed Jun 19, 2019 5:45 pm
VJesus12 wrote:In how many different ways can 3 fiction books and 3 non-fiction books be arranged in a row of 6 books on a shelf such that the fiction books are not separated, and the non-fiction books are not separated?

A. 24
B. 36
C. 72
D. 144
E. 288

[spoiler]OA=C[/spoiler]

Source: Magoosh

The 3 fiction books can be arranged in 3! = 6 ways. Similarly, the 3 nonfiction books can be arranged in 3! = 6 ways also. Since we can arrange the fiction books before the nonfiction books, or the nonfiction before the fiction books, the number of ways to arrange the 6 books is:

6 x 6 x 2 = 72

Answer: C

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by Brent@GMATPrepNow » Thu Jun 20, 2019 5:11 am
VJesus12 wrote:In how many different ways can 3 fiction books and 3 non-fiction books be arranged in a row of 6 books on a shelf such that the fiction books are not separated, and the non-fiction books are not separated?

A. 24
B. 36
C. 72
D. 144
E. 288

[spoiler]OA=C[/spoiler]

Source: Magoosh
Take the task of arranging the 6 books and break it into stages.

Stage 1: Arrange the 3 fiction books in a row
We can arrange n unique objects in n! ways
So, we can arrange the 3 books in 3! ways (= 6 ways)
So, we can complete stage 1 in 6 ways

Stage 2: Arrange the 3 non-fiction books in a row
We can complete stage 2 in 6 ways

Now that we've arranged the two types of books, we need to determine the order they appear on the shelf (i.e.. fiction-nonfiction or nonfiction-fiction)

Stage 3: Select the order in which the 2 book types appear on the shelf
There are 2 options: fiction-nonfiction or nonfiction-fiction
So, we can complete stage 3 in 2 ways

By the Fundamental Counting Principle (FCP), we can complete all 3 stages (and thus arrange all 6 books) in (6)(6)(2) ways (= 72 ways)

Answer: C

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Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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