A bookseller has two display windows. She plans to display 4

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M7MBA: Moderator; Posts: 2058; Joined: Sun Oct 29, 2017 4:24 am; Thanked: 1 times; Followed by:5 members

A bookseller has two display windows. She plans to display 4

by M7MBA » Sat Dec 14, 2019 4:57 am

A bookseller has two display windows. She plans to display 4 new fiction books in the left window, and 3 new non-fiction books in the right window. Assuming she can put the four fiction books in any order, and separately, the three non-fiction books in any order, how many total configurations will there be for the two display windows?

A. 24
B. 72
C. 144
D. 336
E. 420

[spoiler]OA=C[/spoiler]

Source: Magoosh

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Source: Beat The GMAT — Problem Solving | Sat Dec 14, 2019 4:57 am

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by [email protected] » Sat Dec 14, 2019 3:24 pm

Hi M7MBA,

We're told that a bookseller has two display windows - and she plans to display 4 new fiction books in the left window and 3 new non-fiction books in the right window. Assuming she can put the four fiction books in any order, and separately, the three non-fiction books in any order, how many total configurations will there be for the two display windows. This is a mid-level Permutation question and requires just a bit of multiplication to solve.

To start, since we are putting the books in order (without any restrictions), we can use basic multiplication (re: factorials) to solve:

For the 4 fiction books, there are 4! = (4)(3)(2)(1) = 24 ways to arrange those books in the window
For the 3 non-fiction books, there are 3! = (3)(2)(1) = 6 ways to arrange those books in the window
In total, we have (24)(6) = 144 different ways to arrange the books.

Final Answer: C

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Wed Jan 01, 2020 6:40 pm

M7MBA wrote:A bookseller has two display windows. She plans to display 4 new fiction books in the left window, and 3 new non-fiction books in the right window. Assuming she can put the four fiction books in any order, and separately, the three non-fiction books in any order, how many total configurations will there be for the two display windows?

A. 24
B. 72
C. 144
D. 336
E. 420

[spoiler]OA=C[/spoiler]

Source: Magoosh

The number of configurations is 4! x 3! = 24 x 6 = 144.

Answer: C

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