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

Author Message
SVP
Joined: 30 Apr 2008
Posts: 1867

Kudos [?]: 615 [0], given: 32

Location: Oklahoma City
Schools: Hard Knocks
There are 9 books on a shelf, 7 hard cover and 2 soft cover. [#permalink]

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19 Jul 2008, 17:48
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

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$$. GMAT Club Premium Membership - big benefits and savings Kudos [?]: 615 [0], given: 32 Director Joined: 10 Sep 2007 Posts: 934 Kudos [?]: 338 [0], given: 0 Re: Combinations Problem - Books selected from a shelf [#permalink] ### Show Tags 19 Jul 2008, 18:07 1st Way: 1 soft cover, 3 hard cover = 7C3 * 2C1 = 7*6*5/3*2 * 2 = 70 2nd Way: 2 soft cover, 2 hard cover = 7C2 * 2C2 = 7*6/2 = 21 Total ways = 70 + 21 = 91 Answer B. Kudos [?]: 338 [0], given: 0 SVP Joined: 30 Apr 2008 Posts: 1867 Kudos [?]: 615 [0], given: 32 Location: Oklahoma City Schools: Hard Knocks Re: Combinations Problem - Books selected from a shelf [#permalink] ### Show Tags 19 Jul 2008, 20:13 You are all correct, OA is B! The way I did this was Total - invalid combinations = Correct Answer. $$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$$. 126 - 35 = 91. jallenmorris wrote: There are 9 books on a shelf, 7 hard cover and 2 soft cover. How many different combinations exist in which you choose 4 books from the 9 and have at least one of them be a soft cover book? a) 126 b) 91 c) 84 d) 70 e) 108 _________________ ------------------------------------ J Allen Morris **I'm pretty sure I'm right, but then again, I'm just a guy with his head up his a$$.

GMAT Club Premium Membership - big benefits and savings

Kudos [?]: 615 [0], given: 32

SVP
Joined: 28 Dec 2005
Posts: 1545

Kudos [?]: 178 [0], given: 2

Re: Combinations Problem - Books selected from a shelf [#permalink]

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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

Kudos [?]: 178 [0], given: 2

Director
Joined: 01 Jan 2008
Posts: 618

Kudos [?]: 198 [0], given: 1

Re: Combinations Problem - Books selected from a shelf [#permalink]

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21 Jul 2008, 12:01

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

Kudos [?]: 198 [0], given: 1

Re: Combinations Problem - Books selected from a shelf   [#permalink] 21 Jul 2008, 12:01
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