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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.
A. 4
B. 6
C. 9
D. 24
E. 36
untitled.JPG [ 4.8 KiB | Viewed 3810 times ]
A. 4
B. 6
C. 9
D. 24
E. 36
Attachment:
untitled.JPG [ 4.8 KiB | Viewed 3810 times ]
08 Mar 2011, 18:50
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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.
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.
General Discussion
08 Mar 2011, 18:26
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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.
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.
