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

Question

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

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

generis · Accepted Answer

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

She chooses 4 books: __ * __ * __ * __

For her first choice she has 10 books to choose from; then she has nine books; then eight; and then seven.

10 * 9 * 8 * 7 = 5040

Answer D

somtsat99 · Answer

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.

BrentGMATPrepNow · Answer

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

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

RELATED VIDEOS
 https://www.youtube.com/watch?v=w5d5bvCRyd4

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niks18 · Answer

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

ScottTargetTestPrep · Answer

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.

Answer: D

EgmatQuantExpert · Answer

Solution

Given:  
 • Clarissa will choose 4 books from the 10 books.
• She will list the books in the order in which they are chosen.

To find:  
 • The number of different possible lists.  
  Approach and Working:

• She is first selecting 4 books and then listing them.
• This is same as selectin and then arrangement. 
o Hence, this a permutation question.
• Thus, total ways=  ^{10}P_4 = 5040.

Hence, option D is the correct answer.

Answer: D

ENEM · Answer

EgmatQuantExpert ,

so if order didn't matter then the answer would be...10!/4!(10-4)! = 210??

EgmatQuantExpert · Answer

Hey  ENEM ,

Yes, if the order does not matter then the total ways will be 210.

You can actually read a lot on this topic in our Permutation and Combination article.

Here is the link of the article:   Fool-proof method to Differentiate between Permutation & Combination Questions

Regards,
Ashutosh
e-GMAT

Farina · Answer

Here AB is not equal to BA because order matters.
Also, Repetition is not allowed so
Permutation formula will be applied. 10!/6! = 5040

GMATinsight · Answer

Answer: Option D

Video solution by  GMATinsight

https://www.youtube.com/watch?v=v1qe9yh3n1o

DanTheGMATMan · Answer

Classic combinatorics we all know and love:

https://www.youtube.com/watch?v=qzVf3BTn0ZY

kaveree · Answer

is the only way to solving combinations and permutations is by manually multiplying the 10x9x8x7 and no other shortcut? because what if the question has a big number like 200!

DanTheGMATMan · Answer

They won't do that to you. The point of the GMAT is to cleverly solve problems, not do big calculations

zhangwma · Answer

In case this is helpful for anyone else, I solved this question in 27 seconds by seeing that I only needed a 4 in the tens place and a 0 in the units place, and of all the answers, only D met that criteria.

Elaboration: 10 x 9 x (8x7) = 10 x 9 x 56 --> 6x9 = 54, so including the factor of ten, we know the answer will be a value with some number of digits before __40.

AbhishekP220108 · Answer

Since, the questions asks for different list, the no. of empty spaces is 4 and total option available is 10. Hence, this is a permutation problem, simply doing 10*9*8*7=5040

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

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