There are 8 books in a shelf that consists of 2 paperback books and 6 hardback books. If 4 books are selected at random without replacement, how many different combinations are there that at least one paperback book is selected?
A. 40
B. 45
C. 50
D. 55
E. 60
The OA is D.
Please, can anyone explain this PS question? I tried to solve it but I can't get the correct answer. I need help. Thanks.
There are 8 books in a shelf that consists of 2 paperback
This topic has expert replies
- GMATGuruNY
- GMAT Instructor
- Posts: 15539
- Joined: Tue May 25, 2010 12:04 pm
- Location: New York, NY
- Thanked: 13060 times
- Followed by:1906 members
- GMAT Score:790
Combinations with at least 1 paperback = (all possible combinations) - (combinations with no paperbacks).swerve wrote:There are 8 books in a shelf that consists of 2 paperback books and 6 hardback books. If 4 books are selected at random without replacement, how many different combinations are there that at least one paperback book is selected?
A. 40
B. 45
C. 50
D. 55
E. 60
The OA is D.
Please, can anyone explain this PS question? I tried to solve it but I can't get the correct answer. I need help. Thanks.
All possible combinations:
From the 8 books, the number of ways to choose 4 = 8C4 = (8*7*6*5)/(4*3*2*1) = 70.
Combinations with no paperbacks:
From the 6 hardback books, the number of ways to choose 4 = 6C4 = (6*5*4*3)/(4*3*2*1) = 15.
Combinations with at least 1 paperback:
70-15 = 55.
The correct answer is D.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
GMAT/MBA Expert
- Jeff@TargetTestPrep
- GMAT Instructor
- Posts: 1462
- Joined: Thu Apr 09, 2015 9:34 am
- Location: New York, NY
- Thanked: 39 times
- Followed by:22 members
We can use the equation:swerve wrote:There are 8 books in a shelf that consists of 2 paperback books and 6 hardback books. If 4 books are selected at random without replacement, how many different combinations are there that at least one paperback book is selected?
A. 40
B. 45
C. 50
D. 55
E. 60
It must be true that:
The number of ways in which at least 1 paperback book is selected = The total number of ways to select 4 books - The number of ways in which no paperback books are selected
The number of ways in which no paperback books are selected is equivalent to the number of ways in which all 4 books selected are hardcover. Let's determine that now. There are 6 hardback books, and 4 must be selected; thus:
6C4 = 6!/(4! x 2!) = (6 x 5)/2! = 30/2 = 15 ways
Now we determine the total number of ways to select the books. There are 8 total books and 4 must be selected, thus:
8C4 = 8!/(4! x 4!) = (8 x 7 x 6 x 5)/4! = 7 x 2 x 5 = 70 ways
Thus, the number of ways to select at least one paperback book = 70 - 15 = 55 ways.
Answer: D
Jeffrey Miller
Head of GMAT Instruction
[email protected]
See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews