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A company that ships boxes to a total of 12 distribution

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Intern
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Joined: 25 May 2008
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A company that ships boxes to a total of 12 distribution [#permalink]

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New post 16 Oct 2008, 13:45
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A company that ships boxes to a total of 12 distribution centers uses color coding to identify each center. If either a single color or a pair of two different colors is chosen to represent each center and if each center is uniquely represented by that choice of one or two colors, what is the minimum number of colors needed for the coding?(Assume that the order of the colors in a pair does not matter)

a. 4
b. 5
c. 6
d. 12
e. 24.

I am assuming this question is to do with permutations and combinations.
Could someone please tell me the answer, and also explain how to solve this kind of question... I got dead confused

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Manager
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Joined: 14 Oct 2008
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Re: PS: Distribution Centres [#permalink]

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New post 16 Oct 2008, 14:30
Is the answer 5 ?
I did not use any particular permutation or com formula.
Consider 2 colours, you can distinguish 3 centers on the basis of that, 1 for each colour and 1 for them together
Similarly, with 3 colours - 3 + 3 = 6 centers.
With 4 colours - 4 single + 3+2+1 = 10 centers
so it has to be 5 colours.

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Re: PS: Distribution Centres [#permalink]

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New post 16 Oct 2008, 17:25
yes, 5 colors

4 individual colors + 4C2=10 centers
since we need to cover 12 centers we need one more color, so with 5 colors we can cover all 12 centers

what is the OA

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Re: PS: Distribution Centres [#permalink]

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New post 16 Oct 2008, 19:23
I get 5 as well

5 + 5C2 will be enough ...

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Re: PS: Distribution Centres   [#permalink] 16 Oct 2008, 19:23
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A company that ships boxes to a total of 12 distribution

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