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# Combinatorics (very difficult)

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Manager
Joined: 22 Jun 2008
Posts: 103
Schools: Darden School of Business (Class of 2012)
Followers: 1

Kudos [?]: 16 [0], given: 1

Combinatorics (very difficult) [#permalink]  08 Sep 2008, 08:39
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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Joined: 07 Nov 2007
Posts: 1824
Location: New York
Followers: 29

Kudos [?]: 564 [1] , given: 5

Re: Combinatorics (very difficult) [#permalink]  08 Sep 2008, 08:46
1
KUDOS
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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Intern
Joined: 27 Aug 2007
Posts: 35
Followers: 1

Kudos [?]: 12 [1] , given: 0

Re: Combinatorics (very difficult) [#permalink]  08 Sep 2008, 08:48
1
KUDOS
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?
Director
Joined: 12 Jul 2008
Posts: 518
Schools: Wharton
Followers: 16

Kudos [?]: 122 [0], given: 0

Re: Combinatorics (very difficult) [#permalink]  08 Sep 2008, 09:28
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
Manager
Joined: 22 Jun 2008
Posts: 103
Schools: Darden School of Business (Class of 2012)
Followers: 1

Kudos [?]: 16 [0], given: 1

Re: Combinatorics (very difficult) [#permalink]  08 Sep 2008, 10:46

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, 10:46
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