Clarissa will create her summer reading list by randomly choosing 4 books from the 10 books approved for summer reading.

[M7MBA]

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

Source: Official Guide

[Brent@GMATPrepNow]

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

Source: Official Guide

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. For more information about the FCP, watch this video: https://www.gmatprepnow.com/module/gmat- ... /video/775

You can also watch a demonstration of the FCP in action: https://www.gmatprepnow.com/module/gmat ... /video/776

Then you can try solving the following questions:

EASY
- https://www.beatthegmat.com/what-should- ... 67256.html
- https://www.beatthegmat.com/counting-pro ... 44302.html
- https://www.beatthegmat.com/picking-a-5- ... 73110.html
- https://www.beatthegmat.com/permutation- ... 57412.html
- https://www.beatthegmat.com/simple-one-t270061.html


MEDIUM
- https://www.beatthegmat.com/combinatoric ... 73194.html
- https://www.beatthegmat.com/arabian-hors ... 50703.html
- https://www.beatthegmat.com/sub-sets-pro ... 73337.html
- https://www.beatthegmat.com/combinatoric ... 73180.html
- https://www.beatthegmat.com/digits-numbers-t270127.html
- https://www.beatthegmat.com/doubt-on-sep ... 71047.html
- https://www.beatthegmat.com/combinatoric ... 67079.html


DIFFICULT
- https://www.beatthegmat.com/wonderful-p- ... 71001.html
- https://www.beatthegmat.com/permutation- ... 73915.html
- https://www.beatthegmat.com/permutation-t122873.html
- https://www.beatthegmat.com/no-two-ladie ... 75661.html
- https://www.beatthegmat.com/combinations-t123249.html


Cheers,
Brent