Gre

[Guest]

jack receives instructions from 12 clients and uses color coding t o identify each client.if either a single color or a pair of two different colors is chosen to represent each client and if each client is uniquely represented by that choice of one or two colors, what is the minimum number of colors needed for coding?

[Paul g Mathew]

even i found it bit tough intially but got it in the end .

Read the question carefully.Here according to question Jack wants to identify 12 different clients using colors. He can use single color or two different color.
If we use single color to identify clients, 12 different colors we have to use.If we use 2 different colors to identify 12 clients , the number of color required will further
reduce as using combinations we can get more options.So according to question, they want the minimum number of colors required to identify 12 peoples, which can be accomplished using two colors.
what i have understood from question is that we have to select 2 colors from a set of minimum X colors which will help us to identify 12 clients .

ie 2 selected from X should give us 12 different arrangement, and since arrangement does not matter , use combination.

so we will get the answer by solving XC2 = 12

X!/(2!*(X-2)!) = 12

X(X-1)/2 = 12

hence X =5,
so minimum of 5 colors needed for identifying 12 different people

[Guest]

even i found it bit tough intially but got it in the end .

Read the question carefully.Here according to question Jack wants to identify 12 different clients using colors. He can use single color or two different color.
If we use single color to identify clients, 12 different colors we have to use.If we use 2 different colors to identify 12 clients , the number of color required will further
reduce as using combinations we can get more options.So according to question, they want the minimum number of colors required to identify 12 peoples, which can be accomplished using two colors.
what i have understood from question is that we have to select 2 colors from a set of minimum X colors which will help us to identify 12 clients .

ie 2 selected from X should give us 12 different arrangement, and since arrangement does not matter , use combination.

so we will get the answer by solving XC2 = 12

X!/(2!*(X-2)!) = 12

X(X-1)/2 = 12

hence X =5,
so minimum of 5 colors needed for identifying 12 different people

How does x=5 in the the equation x(x-1)/2=12?
If you substitute 5 in the equation you will get 5(4)/2=12 => 10=/=12