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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.

Re: Notepad packaging [#permalink]
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.

Re: Notepad packaging [#permalink]
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

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