combinaTION : GMAT Problem Solving (PS)
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# combinaTION

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Manager
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Joined: 04 Feb 2010
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Concentration: Social Entrepreneurship, Social Entrepreneurship
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17 Oct 2010, 01:03
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Difficulty:

(N/A)

Question Stats:

33% (00:00) correct 67% (00:00) wrong based on 3 sessions

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Dan has a membership at a local gym that also gives classes three nights a week. On any given
class night, Dan has the option of taking yoga, weight training, or kickboxing classes. If Dan
decides to go to either one or two classes per week, how many different combinations of
classes are available?
A. 3
B. 6
C. 7
D. 9
E. 12
[Reveal] Spoiler: OA
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18 Oct 2010, 16:46
i GOT ANSWER AS 6...

C(3,1)+C(3,2)=6
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18 Oct 2010, 19:25
Sounds right to me, either choose 1 or choose 2. Three ways each.

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Manager
Status: GMAT Preperation
Joined: 04 Feb 2010
Posts: 103
Concentration: Social Entrepreneurship, Social Entrepreneurship
GPA: 3
WE: Consulting (Insurance)
Followers: 2

Kudos [?]: 147 [0], given: 15

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19 Oct 2010, 04:55
D. This problem is best done by brute force. First, we must establish that Dan has the option
of taking one or two classes per week. If he only takes one class, the three possibilities are Y, W,
and K. If he takes two classes per week, the six possibilities are YY, KK, WW, YK, YW, and WK
(because the problem is looking for combinations, not arrangements). So that adds up to nine
possible combinations.
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19 Oct 2010, 06:58
This question can be interpreted in different ways:

1. One way is that on one week night, only one class is offered
Selecting 1 class: 3 choices available so 3 ways (or 3C1 = 3)
Selecting 2 classes: Out of 3 classes, 2 need to be selected or we can say, 1 needs to be dropped. This can be done in 3 ways (or 3C2 = 3).
Total 6 ways.

2.i. The gym offers classes 3 nights a week (assume Mon, Wed, Fri). On ANY given class night, options of Yoga, WT or KB are available.
If we want to find the combination of classes only, not days, we can do it in the following way:
Selecting 1 class: 3 choices available so 3 ways (or 3C1 = 3)
Selecting 2 classes: Out of 3 classes, we need to choose 2 This can be done in 3 ways (or 3C2). Since we can choose the same class on both the days, we have another 3 ways.
Total 9 ways.

2.ii. If we want to find the combination of days and classes, we can do it in the following way:
Selecting 1 class: First we choose a day for which we have 3 options (or 3C1) and then we choose one of the 3 classes for which we again have 3 options (or 3C1) and hence we choose in 3x3 = 9 ways
Selecting 2 classes: First we choose 2 days out of 3 in 3 ways (or 3C2). Then we choose a class for the first day in 3 ways and choose a class for the second day in 3 ways. In all, we can choose 2 classes in 3x3x3 = 27 ways.
Total 36 ways.

Now the question is which method to use here. 2.ii. is anyway not possible since the answer options do not have 36. It would be more reasonable to go with 2.i. since the question says "On any given
class night, Dan has the option of taking yoga, weight training, or kickboxing classes".
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Re: combinaTION   [#permalink] 19 Oct 2010, 06:58
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# combinaTION

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