John has 12 clients and he wants to use color coding to identify each client. If either a single color or a pair of two different colors can represent a client code, what is the minimum number of colors needed for the coding? Assume that changing the color order within a pair does not produce different codes.  Pick:  A) 24  B) 12  C) 7  D) 6  E) 5
5 different colours = 5 single colours = 5 different clients   There are 7 clients to go   The use of the factorial is the easiest way to solve this kind of problem for me.   A B C D 5 (different colour)   C C N N N (2 colour coding + 3 colour non chosen)   5!/2!3!= 10   15 codings can be done with 5 different colours   Ans 5
<result>E</result>
John has 12 clients and he wants to use color coding to identify each client. If either a single color or a pair of two different colors can represent a client code, what is the minimum number of colors needed for the coding? Assume that changing the color order within a pair does not produce different codes.