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
OA D
Source: Official Guide
Clarissa will create her summer reading list by randomly
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Since the reading list lays importance to order of the books, we will apply Permutation and not Combination. In other words, if Clarissa chooses A, B, C, and D as chosen 4 books, for example, ABCD and ADCB are two different lists.BTGmoderatorDC 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
OA D
Source: Official Guide
So, the number of ways to choose 4 books (Order in important) = 10P4 = 10.9.8.7 = 5040.
The correct answer: D
Hope this helps!
-Jay
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Take the task of creating the reading list and break it into stages.BTGmoderatorDC 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
OA D
Source: Official Guide
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
Note: the FCP can be used to solve the MAJORITY of counting questions on the GMAT. For more information about the FCP, watch our free video: https://www.gmatprepnow.com/module/gmat- ... /video/775
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DIFFICULT
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Cheers,
Brent
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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.BTGmoderatorDC 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
Answer: D
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