Wednesday, September 22, 2010

A company that ships boxes to a total of 12 distribution centers uses color coding to identify each center. IF either a single color a pair of two different colors is chosen to represent each center and if each center is uniquely repsented by that chocie of one or two colors, what is the minimum number of colors needed for the coding? (assume that order of the colors in a pair does not matter)

A)4
B)5
C)6
D)12
E)24




Since we know order doesn't matter, Hence:
Total possible combinations = Individual color + combination of two colors
Now if we pick three colors
Total possible combinations = 3 + 3!/2! = 3+3 = 6
Now pick four colors
Total possible combinations = 4+ 4!/2!2! = 4+6 = 10
Now pick 5 colors
Total possible combinations = 5 + 5!/3!2! = 5 + 10 = 15 (Sufficient)
Answer is (B)

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