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
OG Clarissa will create her summer reading list
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Number of options for the first book = 10. (Any of the 10 books.)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 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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Take the task of creating the reading list and break it into stages.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
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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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.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
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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
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