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color codes

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color codes

by vittalgmat » Thu Jan 01, 2009 3:38 am
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.

A. 24
B. 12
C. 7
D. 6
E. 5

[spoiler]OA: E[/spoiler]
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by piyush_nitt » Thu Jan 01, 2009 4:00 am
minimum number of ways in which clients can be coded =

single colours + combination of 2 colours

You can eliminate the choices A and B.

Say If John takes 4 single colours than various combinations of colours would be

4C2 = 6

i.e total (single + combination , 4+6)= 10 , that doesnot statisfy the condition.

if single colours = 5

5C2 = 10

i.e total = 15 that statisy the condition.

therefore minimum number of colours required = 5
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