Combinations

[lurkman]

A certain office supply store stocks 2 sizes of self stick pads, each in 4 colors: blue, green, yellow or pink. The store packs the note pads in packages that contain either 3 note pads of the same size and same color or 3 note pads of the same size and of 3 different colors. If the order in which the colors are packed is not considered, how many different packages of the types described above are possible?

(A) 6
(B) 8
(C) 16
(D) 24
(E) 32

Looks simple enough but I got this wrong. My reasoning still doesn't converge to the correct answer.

Any help would be appreciated.

I'll withhold the answer for a while, so as not to spoil the first efforts of those who may want to give this a shot.

lurkman

[lurkman]

Okay, I got it soon after posting this!

lurkman

[Lhomme]

I think it should be

2*(4C1) + 2*(4C3) = 16. Is it C. If the answer matches then I can explain my logic.

[Lhomme]

Okay, I got it soon after posting this!

lurkman

what is the Official Answer ?

[lurkman]

Lhomme, you are right.

Official Answer = (C) or 16.

Our logic is probably the same:

Number of ways to assemble a 3-pack of the same color = 4C1
Number of ways to assemble a 3-pack of different colors = 4C3

2 sizes apply in both cases.

Therefore, 2 * 4C1 + 2 * 4C3 = 2*4 + 2*4 = 16.

My earlier mistake (I did this in the GMAT Prep1):

In my haste, I multiplied 4C1*4C3 and then multiplied by 2 (for the sizes) giving an incorrect answer of 32. (And sure enough, one of the answer choices was 32, which is the kind of trap that GMAC is very good at laying.)

lurkman

[mickgreen58]

Good problem and for once I was able to solve

First criterion doesn't seem to require an Equation:8
Second criterion:2*4C3 = 4*2 = 8
16

[chelsfdu]

Good problem and for once I was able to solve

First criterion doesn't seem to require an Equation:8
Second criterion:2*4C3 = 4*2 = 8
16

I feel the same way.. for once I was actually able to solve