IMO E

The question is asking what is the minimum number of combination of 1 paint or 2 paints possible

i.e. its asking for the minimum value for xC1+xC2>12-----equ1

Now the combination has to be greater than 12 since that is the total number of clients

The answer is 5

5C1 + 5C2 = 5+10 = 15

You can clearly rule out 12 and 24 since they will give you really high values for equ1.

yes, it should be 5 colors

Mals24 - I'm not sure if I understand your explanation. Could you please clarify? What do these equations mean? Thanks!

xC1+xC2>12
5C1 + 5C2 = 5+10 = 15

@ssy

The question is asking us what is the "minimum" number of colors needed for coding. And we can either assign a single color to a client or use two different colors.

In other words the question is asking us what is the minimum number of combination of one or two color codes.

So we set up the equation nC1+nC2>12 (this requires the use of combination and not permutation since the order of colors does not matter)

nC1 is the number of ways we can assign one color to the client
nC2 is the number of ways we can assign two diff colors to the client
+ since its "or"
">12" since the combination should be greater than 12
It cannot be less than 12 since we have a total of 12 clients and we have to find the "minimum" number of color combination. Hence the greater sign

Now we need to see among the answer choices which choice when substituted in place of "n" gives us the least value in the equation.

I hope you get the logic