Problem Solving

A secretary differentiates Â…files by a variety of color combinations. If she uses 4 different colors, and marks each fiÂ…le with 1, 2, or 3 of the colors, how many different color combinations can she generate?

(A) 4
(B) 12
(C) 14
(D) 15
(E) 24

Let the Colors Be A,B,C and D.

Three possibilities.

1 Color to Identify each file. - Each color to identify every file. 4 Ways. (4C1 Ways)

2 Colors to Identify each file -
Here the order of the color matters. Since order matters we have to proceed with permutation.
4P2 ways= 12 ways

(AB,BA, CD,DC, BC,CB,AD,DA,AC,CA,BD,DA)


3 Colors to Identify each file -
Here also the order of the color matters. Since order matters we have to proceed with permutation again.

4P3 ways = 24 ways

(ABC - This color combination can be arranged in 3! ways = 6 Ways)
(BCD - This color combination can be arranged in 3! Ways = 6 ways)
(ABD - This color combination can be arranged in 3! Ways = 6 ways)
(ACD - This color combination can be arranged in 3! ways = 6 ways)

Summing it up 24+12+4 = 40 Ways.
I get atleast 40 ways.
I dont know what else i am missing.
Can anybody help??
Thanks

Tried solving for both combos and for perms because was confused about the answer choices:

I'm getting 14 if order doesn't matter
If order matters I'm getting the same as Junegmat with 40

Don't think I missed anything....
OA?

rros0770 wrote:Tried solving for both combos and for perms because was confused about the answer choices:

I'm getting 14 if order doesn't matter
If order matters I'm getting the same as Junegmat with 40

Don't think I missed anything....
OA?

You are right, Even i am also getting 14,
4C1 = 4
4C2 = 6
4C3 = 4

In all 14

I don't think sequence will matter over here.........

What's the source of this question?

Usually the stem of a question should indicate whether order matters or not. This one sounds as if it doesn't (the word combinations is a hint, though).

Also, I am very confused by the answer choices. This might be just a technicality, but usually the answer choices (provided they consist of numbers) are presented in an ascending order!

jaymw wrote:What's the source of this question?

Usually the stem of a question should indicate whether order matters or not. This one sounds as if it doesn't (the word combinations is a hint, though).

Also, I am very confused by the answer choices. This might be just a technicality, but usually the answer choices (provided they consist of numbers) are presented in an ascending order!

you are all right, it was mistyped - correct answer is C 14