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# There are 8 books in a shelf that consist of 2 paperback

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Manager
Joined: 23 Dec 2013
Posts: 137
Location: United States (CA)
GMAT 1: 710 Q45 V41
GMAT 2: 760 Q49 V44
GPA: 3.76
Re: There are 8 books in a shelf that consist of 2 paperback  [#permalink]

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16 Jul 2017, 11:42
2
pretttyune wrote:
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

There are two scenarios that fit the question: either one paperback or two is selected.

If one is selected, then the total number of combinations is 2C1*6C3 + 2C2*6C2

2C1*6C3:
2*6!/(3!*3!) = 2*6*5*4/3*2 = 40

2C2*6C2
1*6*5*4*3*2/(2*4*3*2) = 15

40+15 =55
Intern
Joined: 20 May 2018
Posts: 5
Re: There are 8 books in a shelf that consist of 2 paperback  [#permalink]

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08 Jul 2018, 01:07
Could someone provide a group of similar Permutation and combination practice problems? Would really appreciate the help
Intern
Joined: 20 May 2018
Posts: 5
Re: There are 8 books in a shelf that consist of 2 paperback  [#permalink]

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08 Jul 2018, 01:09
Could someone provide a group of similar practice problems? Would really appreciate the help on this. Thanks
Math Expert
Joined: 02 Sep 2009
Posts: 59712
Re: There are 8 books in a shelf that consist of 2 paperback  [#permalink]

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10 Jul 2018, 02:21
1
Intern
Joined: 20 May 2018
Posts: 5
Re: There are 8 books in a shelf that consist of 2 paperback  [#permalink]

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11 Jul 2018, 08:51
Thank you! Bunuel
Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2809
Re: There are 8 books in a shelf that consist of 2 paperback  [#permalink]

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14 Jul 2018, 19:39
1
pretttyune wrote:
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

We can use the equation:

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.

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Re: There are 8 books in a shelf that consist of 2 paperback  [#permalink]

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24 Jul 2019, 15:52
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Re: There are 8 books in a shelf that consist of 2 paperback   [#permalink] 24 Jul 2019, 15:52

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