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Manager
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Joined: 10 Mar 2011
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Location: United States (TX)
Concentration: Finance, Economics
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WE: Information Technology (Consulting)
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Kudos [?]: 61 [0], given: 3

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16 Aug 2011, 10:59
00:00

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Question Stats:

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[highlight]A store stocks 2 sizes of notepads, each in 4 colors: blue, green, yellow and pink. The store packs the notepads in packages that contain either 3 notepads of the same size and same color or 3 notepads of the same size and of 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?[/highlight]

Lets say we have 2 size - Large (L) and Small (S).
We have 4 colors for each notepad - B, G, Y and P.

So we have 8 notepads to be packaged in following combination -
either 3 notepads of the same size and same color or 3 notepads of the same size and of different colors.

But with available 8 notepads the only possible combination is "3 notepads of the same size and of different colors".

"3 notepads of the same size and same color" combination was only possible if we had information such as - 4 B, 4 G, 4 Y and 4 P for each size.

Am I missing something?

Ans is 16.

Thanks
Sumeet
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Concentration: Strategy, Finance
Schools: Tuck '16, Darden '16
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16 Aug 2011, 12:00
vatsas wrote:
[highlight]A store stocks 2 sizes of notepads, each in 4 colors: blue, green, yellow and pink. The store packs the notepads in packages that contain either 3 notepads of the same size and same color or 3 notepads of the same size and of 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?[/highlight]

Lets say we have 2 size - Large (L) and Small (S).
We have 4 colors for each notepad - B, G, Y and P.

So we have 8 notepads to be packaged in following combination -
either 3 notepads of the same size and same color or 3 notepads of the same size and of different colors.

But with available 8 notepads the only possible combination is "3 notepads of the same size and of different colors".

"3 notepads of the same size and same color" combination was only possible if we had information such as - 4 B, 4 G, 4 Y and 4 P for each size.

Am I missing something?

Ans is 16.

Thanks
Sumeet

I did it without looking at your answer and got the same thing.

8 packs where all note pads are the same colour, and then 4C3*2 where they are different colours = 16

If that is not OA, then I guess they are considering Blue, Blue, Green as a possible combination, but IMO as written that is not a possibility.
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16 Aug 2011, 12:31
vatsas wrote:
[highlight]A store stocks 2 sizes of notepads, each in 4 colors: blue, green, yellow and pink. The store packs the notepads in packages that contain either 3 notepads of the same size and same color or 3 notepads of the same size and of 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?[/highlight]

Lets say we have 2 size - Large (L) and Small (S).
We have 4 colors for each notepad - B, G, Y and P.

So we have 8 notepads to be packaged in following combination -
either 3 notepads of the same size and same color or 3 notepads of the same size and of different colors.

But with available 8 notepads the only possible combination is "3 notepads of the same size and of different colors".

"3 notepads of the same size and same color" combination was only possible if we had information such as - 4 B, 4 G, 4 Y and 4 P for each size.

Am I missing something?

Ans is 16.

Thanks
Sumeet

Since there are just 16 possibilities, I'll write them all up:

We have 4 colors:
blue, green, yellow and pink
Small-S
Large-L

SSS
SSS
SSS
SSS
LLL
LLL
LLL
LLL
SSS
SSS
SSS
SSS
LLL
LLL
LLL
LLL

Or simply,
We have 4 colors AND 2 sizes
OR
We have 4 colors(select 3) AND 2 sizes

$$4*2+C^4_3*2=16$$
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21 Aug 2011, 08:23
same size same color = (2*4)*1*1 = 8

same size different color (color order doesn't matter as per the question.)

= 2*4c3 = 8

total possible packages = 8+8 = 16
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