OG Clarissa will create her summer reading list

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AbeNeedsAnswers: Master | Next Rank: 500 Posts; Posts: 394; Joined: Sun Jul 02, 2017 10:59 amFollowed by: 5 members; Thanked: 1 times

by AbeNeedsAnswers » Fri Aug 18, 2017 5:54 pm

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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

D

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Source: Beat The GMAT — Problem Solving | Fri Aug 18, 2017 5:54 pm

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by GMATGuruNY » Sat Aug 19, 2017 2:46 am

AbeNeedsAnswers 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

Number of options for the first book = 10. (Any of the 10 books.)
Number of options for the second book = 9. (Any of the 9 remaining books.)
Number of options for the third book = 8. (Any of the 8 remaining books.)
Number of options for the fourth book = 7. (Any of the 7 remaining books.)
To combine these options, we multiply:
10*9*8*7 = 5040.

The correct answer is D.

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OG Clarissa will create her summer reading list

by Brent@GMATPrepNow » Sat Aug 19, 2017 6:43 pm

AbeNeedsAnswers 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

D

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: D

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by Scott@TargetTestPrep » Thu Nov 16, 2017 7:14 am

AbeNeedsAnswers 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

Since the order of the books in her list matters, we use permutation. Thus, the number of ways 4 books can be chosen and ordered from 10 books is 10P4 = 10!/(10-4)! = 10 x 9 x 8 x 7 = 5,040.

D

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[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » Sun Jun 10, 2018 5:07 pm

Hi All,

We're told that Clarissa will create her summer reading list by randomly choosing 4 books from the 10 books approved for summer reading and she will list the books in the order in which they are chosen. We're asked for the number of different lists that are possible. The 'math' behind this question is fairly straight-forward - and the Answers are 'spread out' enough that you can avoid doing the entire calculation.

Since Clarissa can't choose a book more than once, once she chooses a book, there will be 1 fewer option for the next book. Thus, there will be (10)(9)(8)(7) possible orders of the four books. By comparison, we know that (10)(10)(10)(10) = 10,000 is clearly bigger than that total... and by rewriting the total as (90)(56) you should be able to recognize that it is far larger than 210. There's only one answer that 'fits' that range...

Final Answer: D

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

Contact Rich at [email protected]

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