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Combinatorics (very difficult)

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Combinatorics (very difficult) [#permalink] New post 08 Sep 2008, 09:39
Hi guys, I made a gmat prep yesterday and score more than 700. I need help with the following problem:

"A certain office supply store stocks 2 sizes of self stick notepads, each in 4 colors, blue, green, yelow or pink. The store packs the notepad in packages that contain either 3 notepads of the same size and of the same color or 3 notepads 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
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Re: Combinatorics (very difficult) [#permalink] New post 08 Sep 2008, 09:46
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lordw wrote:
Hi guys, I made a gmat prep yesterday and score more than 700. I need help with the following problem:

"A certain office supply store stocks 2 sizes of self stick notepads, each in 4 colors, blue, green, yelow or pink. The store packs the notepad in packages that contain either 3 notepads of the same size and of the same color or 3 notepads 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


B G Y P -- Size 1
b g y p -- Size 2

For Size -1:
No . of ways 3 notepads of the same size and of the same color = 4 (BBB,GGG, YYY, PPP)
No . of ways 3 notepads of the same size and of 3 different colors= 4C3 (BGY,PGY, YPB, BPG)

For size -1 = 4+4C3 = 8
similarly For size -2 = 4+4C3 = 8

Total =16
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Re: Combinatorics (very difficult) [#permalink] New post 08 Sep 2008, 09:48
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3 notepads of the same size and of the same color
4(colors) * 2 (sizes) = 8

3 notepads of the same size and of 3 different colors
4C3 (colors) * 2 (sizes) = 8

Total = 16 (C).

OA?
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Re: Combinatorics (very difficult) [#permalink] New post 08 Sep 2008, 10:28
lordw wrote:
Hi guys, I made a gmat prep yesterday and score more than 700. I need help with the following problem:

"A certain office supply store stocks 2 sizes of self stick notepads, each in 4 colors, blue, green, yelow or pink. The store packs the notepad in packages that contain either 3 notepads of the same size and of the same color or 3 notepads 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


Same size and same color = 2*4 = 8
Same size and 3 different colors = 2*(4C3) = 8
Total = 8 + 8 = 16
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Re: Combinatorics (very difficult) [#permalink] New post 08 Sep 2008, 11:46
OA is your answer, regards and tks!

lkothari wrote:
3 notepads of the same size and of the same color
4(colors) * 2 (sizes) = 8

3 notepads of the same size and of 3 different colors
4C3 (colors) * 2 (sizes) = 8

Total = 16 (C).

OA?
Re: Combinatorics (very difficult)   [#permalink] 08 Sep 2008, 11:46
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