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Regions and Colors

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Intern
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Joined: 16 Jan 2011
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Regions and Colors [#permalink] New post 08 Mar 2011, 17:22
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

50% (00:00) correct 50% (00:00) wrong based on 2 sessions
Following are the four regions 1,2,3 and 4 and they need to be colored with 3 different colors but no two adjacent regions can have same color. For example, region 1 3 and 4 can be colored with same color and region 2 with a different color. How many such color combination exist with which the region can be colored.
[img]untitled.JPG[/img]

a) 4
b) 6
c) 9
d) 24
e) 36
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Director
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Re: Regions and Colors [#permalink] New post 08 Mar 2011, 17:26
1234
I can choose 4C3 colors and these three colors can be ordered in 3! ways. So 4! combination. The answer has to be more than 4!. Hence I will guess E.
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Re: Regions and Colors [#permalink] New post 08 Mar 2011, 17:50
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You have:

3 choices for the color of region 1
2 choices for the color of region 2 (must be different from region 1)
2 choices for the color of region 3 (must be different from region 2)
2 choices for the color of region 4 (must be different from region 2)

Multiplying your choices gives 3*2*2*2 = 24 colorings in total.
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Director
Director
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Status: Matriculating
Affiliations: Chicago Booth Class of 2015
Joined: 03 Feb 2011
Posts: 932
Followers: 11

Kudos [?]: 180 [0], given: 123

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Re: Regions and Colors [#permalink] New post 08 Mar 2011, 18:29
thanks Ian - yes I misinterpreted. This question is resisting any straight formulas or formal approach.

IanStewart wrote:
You have:

3 choices for the color of region 1
2 choices for the color of region 2 (must be different from region 1)
2 choices for the color of region 3 (must be different from region 2)
2 choices for the color of region 4 (must be different from region 2)

Multiplying your choices gives 3*2*2*2 = 24 colorings in total.
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Re: Regions and Colors [#permalink] New post 08 Mar 2011, 20:58
The answer is 24 (choice D).
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Re: Regions and Colors   [#permalink] 08 Mar 2011, 20:58
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