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Clarissa will create her summer reading list by randomly choosing 4 bo

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Clarissa will create her summer reading list by randomly choosing 4 bo [#permalink]

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Clarissa will create her summer reading list by randomly choosing 4 books from the 10 books approved for summer reading. She will list the books in the order in which they are chosen. How many different lists are possible?

A. 6
B. 40
C. 210
D. 5,040
E. 151,200




The Official Guide for GMAT Review 2018

Practice Question
Problem Solving
Question No.: 140
[Reveal] Spoiler: OA

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Clarissa will create her summer reading list by randomly choosing 4 bo [#permalink]

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AbdurRakib wrote:
Clarissa will create her summer reading list by randomly choosing 4 books from the 10 books approved for summer reading. She will list the books in the order in which they are chosen. How many different lists are possible?

A. 6
B. 40
C. 210
D. 5,040
E. 151,200

The Official Guide for GMAT Review 2018

Practice Question
Problem Solving
Question No.: 140

Using the fundamental counting principle (or permutation, because order matters -- she's listing them in their order chosen):

For her first book she has 10 to choose from, then nine, than eight, then seven.

10 * 9 * 8* 7 = 5040

Answer D

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Re: Clarissa will create her summer reading list by randomly choosing 4 bo [#permalink]

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New post 27 Jun 2017, 15:26
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AbdurRakib wrote:
Clarissa will create her summer reading list by randomly choosing 4 books from the 10 books approved for summer reading. She will list the books in the order in which they are chosen. How many different lists are possible?

A. 6
B. 40
C. 210
D. 5,040
E. 151,200


Take the task of creating the reading list and break it into stages.


Stage 1: Select a book to read 1st
There are 10 books to choose from. So, we can complete stage 1 in 10 ways

Stage 2: Select a book to read 2nd
There are 9 books remaining to choose from (since we already chose a book in stage 1).
So, we can complete stage 2 in 9 ways

Stage 3: Select a book to read 3rd
There are 8 books remaining to choose from. So, we can complete stage 3 in 8 ways

Stage 4: Select a book to read 4th
There are 7 books remaining to choose from. So, we can complete stage 4 in 7 ways

By the Fundamental Counting Principle (FCP), we can complete all 4 stages (and thus create a reading list) in (10)(9)(8)(7) ways (= 5040 ways)

Answer:
[Reveal] Spoiler:
D


Note: the FCP can be used to solve the MAJORITY of counting questions on the GMAT. So, be sure to learn it.

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Re: Clarissa will create her summer reading list by randomly choosing 4 bo [#permalink]

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New post 29 Jun 2017, 00:09
4 books can be chosen as 10C4 ways. = 210 ways
Total list of 4 books = 4!
Therefore, total list of possible selection = 210 *4! = 210 *24 =5,040.

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Re: Clarissa will create her summer reading list by randomly choosing 4 bo [#permalink]

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New post 08 Aug 2017, 23:45
AbdurRakib wrote:
Clarissa will create her summer reading list by randomly choosing 4 books from the 10 books approved for summer reading. She will list the books in the order in which they are chosen. How many different lists are possible?

A. 6
B. 40
C. 210
D. 5,040
E. 151,200




The Official Guide for GMAT Review 2018

Practice Question
Problem Solving
Question No.: 140


as the order is important here, so its a Permutation case. So arranging 4 books out of 10 books is
\(10_P_4\) = 5040

Option D

Kudos [?]: 86 [0], given: 27

Re: Clarissa will create her summer reading list by randomly choosing 4 bo   [#permalink] 08 Aug 2017, 23:45
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