Task: Question Answering
Input (English): Problem: 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 ) 
Options: a ) 4 , b ) 5 , c ) 6 , d ) 12 , e ) 24
Output (English): b