Probability... requesting explanation please!

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This question came from kaplan..

A "complete set" of disks consists of one green disk, one blue disk, one orange disk, and one purple disk. A bag contains 12 green disks, 12 blue disks, 12 orange disks, and 12 purple disks. The bag contains nothing else. If 6 disks are randomly selected from the bag, what is the greatest possible number of complete sets of disks that could be remaining in the bag?

a 5
b 6
c 8
d 9
e 10


What formula is this? I'm hoping for mathmatical equation to understand this! thanks,

[spoiler]OA-e
In order to solve this problem we must think about how to maximize the number of complete sets of disks that will remain in the bag. If all 6 disks removed are orange, then there will only be 6 orange disks remaining in the bag. Since there will be 12 blue disks, 12 orange disks, and 12 purple disks remaining in the bag, it will only be possible to select 6 complete sets of disks. So to maximize the number of complete sets remaining in the bag, we should remove a complete set consisting of one green disk, one blue disk, one orange disk, and one purple disk, and then 2 more disks that are of different colors. This will leave 10 complete sets of disks in the bag. There will also be 2 additional different disks. Therefore choice (E) is the correct answer.[/spoiler][/spoiler]
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by cramya » Thu Dec 04, 2008 9:53 pm
An algebric or formula based approach(may be there is one) is not coming to my mind.

I would go wiht maximising the disks possible approach! I read the solution after that and it is along the same lines.

I am sure other brialliant minds on this forum may have a formula approach!

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Okay - first of all, you DO NOT need an equation for this question. This is a GMAT test, not a calculus midterm.

12 12 12 12
11 11 11 11 ( after you pick 1 from each) and you are left with 11 sets
10 10 11 11 ( now you picked two more and you are left with 10 sets_

That's it! ;-)
LGTCH
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hwiya320 wrote:
Thu Dec 04, 2008 8:13 pm
This question came from kaplan..

A "complete set" of disks consists of one green disk, one blue disk, one orange disk, and one purple disk. A bag contains 12 green disks, 12 blue disks, 12 orange disks, and 12 purple disks. The bag contains nothing else. If 6 disks are randomly selected from the bag, what is the greatest possible number of complete sets of disks that could be remaining in the bag?

a 5
b 6
c 8
d 9
e 10


What formula is this? I'm hoping for mathmatical equation to understand this! thanks,

To maximize the number of complete sets in the bag, we should minimize the number of disks selected of each color. Since we are choosing 6 disks and since there are 4 available colors, we should select 2 disks of the same color for 2 colors and 1 disk of each of the remaining colors.

If we removed, for instance, 2 green, 2 blue, 1 orange, and 1 purple disks, the remaining disks would be:

10 green, 10 blue, 11 orange, and 11 purple disks, from which we could make 10 complete sets.

Answer: E

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