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GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2508
Given Kudos: 1053
GPA: 3.39
There are 8 books in a shelf that consist of 2 paperback books and 6 h
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29 Nov 2022, 08:32
29 Nov 2022, 08:32
Expert Reply
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Question Stats:
50% (01:53) correct
50% (02:13) wrong based on 4 sessions
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There are 8 books in a shelf that consist 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
A. 40
B. 45
C. 50
D. 55
E. 60
GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2508
Given Kudos: 1053
GPA: 3.39
Re: There are 8 books in a shelf that consist of 2 paperback books and 6 h
[#permalink]
30 Nov 2022, 22:48
30 Nov 2022, 22:48
1
Expert Reply
There are 8 books on a shelf that consist 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?
Solution:
No. of combinations that have atleast one paperback is
= Total no. of combinations - Combinations in which there is no paperback
= 8C4 - 6C4
= 55 ways
Another way of doing this is finding out directly
No. of combinations that have atleast one paperback is
= Total no. of combinations that have 2 paperback + total no. of combinations that have 1 paperback
= 2C2 * 6C2 + 2C1 * 6C3
= 15 + 40
= 55 ways
Answer: D
Solution:
No. of combinations that have atleast one paperback is
= Total no. of combinations - Combinations in which there is no paperback
= 8C4 - 6C4
= 55 ways
Another way of doing this is finding out directly
No. of combinations that have atleast one paperback is
= Total no. of combinations that have 2 paperback + total no. of combinations that have 1 paperback
= 2C2 * 6C2 + 2C1 * 6C3
= 15 + 40
= 55 ways
Answer: D
gmatclubot
Re: There are 8 books in a shelf that consist of 2 paperback books and 6 h [#permalink]
30 Nov 2022, 22:48
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