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