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PS GMAT prep Probability

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Manager
Joined: 19 Oct 2008
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PS GMAT prep Probability [#permalink]  23 Mar 2009, 10:07
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A certain office supply store stocks 2 sizes of note pads, each in 4 colors (blue, green, yellow or pink). The store packs the notepads in packages that contain either 3 notepads of the same size and the same color or three notepads of the same size and three different colors. If the order in which the colors are packed is not considered, how many different packages of the type described above are possible.

A. 6
B. 8
C. 16
D. 24
E. 32
Senior Manager
Joined: 06 Mar 2006
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Re: PS GMAT prep Probability [#permalink]  23 Mar 2009, 11:52
Accountant wrote:
A certain office supply store stocks 2 sizes of note pads, each in 4 colors (blue, green, yellow or pink). The store packs the notepads in packages that contain either 3 notepads of the same size and the same color or three notepads of the same size and three different colors. If the order in which the colors are packed is not considered, how many different packages of the type described above are possible.

A. 6
B. 8
C. 16
D. 24
E. 32

Two different size of note pads and each in 4 colors.
So there are 4 note pads in one size and 4 note pads in the other size.
From the 4 of the same size and different color to chose 3, there will be 4 different ways. 4!/(3!(4-3)!)=4
From the 4 of the other size and different color to chose 3, there will again be 4 ways.
There is no way the package can be the same size and same color.
So the number of ways will be 4+4=8, or answer B.
Manager
Joined: 19 Oct 2008
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Re: PS GMAT prep Probability [#permalink]  23 Mar 2009, 14:17
OA is C. Can you please try again?
CEO
Joined: 17 Nov 2007
Posts: 3578
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
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Re: PS GMAT prep Probability [#permalink]  23 Mar 2009, 14:37
Expert's post
4 = $$C^4_3$$ - packages with notepads of different colors.
4 = $$C^4_1$$ - packages with notepads of the same color
x2 - for each size

(4+4) x 2 = 16 (C)
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Re: PS GMAT prep Probability   [#permalink] 23 Mar 2009, 14:37
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