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There are 9 books on a shelf, 7 hard cover and 2 soft cover.

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Joined: 30 Apr 2008
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There are 9 books on a shelf, 7 hard cover and 2 soft cover. [#permalink] New post 19 Jul 2008, 17:48
There are 9 books on a shelf, 7 hard cover and 2 soft cover. How many different combinations exist in which you choose 4 books from the 9 and have at least one of them be a soft cover book?

a) 126
b) 91
c) 84
d) 70
e) 108
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J Allen Morris
**I'm pretty sure I'm right, but then again, I'm just a guy with his head up his a$$.

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Re: Combinations Problem - Books selected from a shelf [#permalink] New post 19 Jul 2008, 18:07
1st Way: 1 soft cover, 3 hard cover = 7C3 * 2C1 = 7*6*5/3*2 * 2 = 70

2nd Way: 2 soft cover, 2 hard cover = 7C2 * 2C2 = 7*6/2 = 21

Total ways = 70 + 21 = 91

Answer B.
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Joined: 30 Apr 2008
Posts: 1900
Location: Oklahoma City
Schools: Hard Knocks
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Re: Combinations Problem - Books selected from a shelf [#permalink] New post 19 Jul 2008, 20:13
You are all correct, OA is B!

The way I did this was Total - invalid combinations = Correct Answer.

C_9^4 = 126. Because we need to have at least 1 soft cover, we need to subtract out all of the instances when we have 4 of the 7 hard covers selected...this is C_7^4 = 35. 126 - 35 = 91.

jallenmorris wrote:
There are 9 books on a shelf, 7 hard cover and 2 soft cover. How many different combinations exist in which you choose 4 books from the 9 and have at least one of them be a soft cover book?

a) 126
b) 91
c) 84
d) 70
e) 108

_________________

------------------------------------
J Allen Morris
**I'm pretty sure I'm right, but then again, I'm just a guy with his head up his a$$.

Find out what's new at GMAT Club - latest features and updates

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Joined: 28 Dec 2005
Posts: 1612
Followers: 1

Kudos [?]: 53 [0], given: 2

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Re: Combinations Problem - Books selected from a shelf [#permalink] New post 21 Jul 2008, 11:21
jallenmorris wrote:
You are all correct, OA is B!

The way I did this was Total - invalid combinations = Correct Answer.

C_9^4 = 126. Because we need to have at least 1 soft cover, we need to subtract out all of the instances when we have 4 of the 7 hard covers selected...this is C_7^4 = 35. 126 - 35 = 91.

jallenmorris wrote:
There are 9 books on a shelf, 7 hard cover and 2 soft cover. How many different combinations exist in which you choose 4 books from the 9 and have at least one of them be a soft cover book?

a) 126
b) 91
c) 84
d) 70
e) 108



exact same way I did it ! Although Im always somewhat nervous about this approach because Im not always certain whether Ive accounted for all possibilities :)
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Re: Combinations Problem - Books selected from a shelf [#permalink] New post 21 Jul 2008, 12:01
I like your solution!

jallenmorris wrote:
You are all correct, OA is B!

The way I did this was Total - invalid combinations = Correct Answer.

C_9^4 = 126. Because we need to have at least 1 soft cover, we need to subtract out all of the instances when we have 4 of the 7 hard covers selected...this is C_7^4 = 35. 126 - 35 = 91.

jallenmorris wrote:
There are 9 books on a shelf, 7 hard cover and 2 soft cover. How many different combinations exist in which you choose 4 books from the 9 and have at least one of them be a soft cover book?

a) 126
b) 91
c) 84
d) 70
e) 108
Re: Combinations Problem - Books selected from a shelf   [#permalink] 21 Jul 2008, 12:01
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