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by sirisha.g » Sun Aug 22, 2010 2:49 am
A company that ships boxes to a total of 12 countries uses color coding to identify each center. If either a single color or a pair of 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 doesn't matter)

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

[spoiler]IMO A because order of the pair doesn't matter. BUT OA: B[/spoiler]
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by hala_absi » Sun Aug 22, 2010 6:00 am
You have 12 countries, therefore you need 12 color combinations of single color or double color.
Start with 3 colors
3 colors make 3 single colors and 3!/2!1! = 3 combinations of double colors = >3+3 = 6 X NOT ENOUGH
4 colors makes 4 single colors and 4!/2!2! = 6 combinations => 4+6 = 10 X NOT ENOUGH
5 colors makes 5 single colors and 5!/2!3! = 10 combinations => 10+5 = 15 are enough for 12 countries.
The answer is the (B) 5

Hope this helps!
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