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GMAT Prep counting prob

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GMAT Prep counting prob

by dv2020 » Fri Jun 03, 2011 10:20 am
A certain office supply store stocks 2 sizes of self-stick notepads, 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 & 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 decribed above are possible?
6
8
16
24
32


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by Frankenstein » Fri Jun 03, 2011 10:28 am
Hi,
Let the size be small(S) and large(L)
A small package can have 3 notepads of different colors in 4C3 ways = 4
A small package can have 3 notepads of same color in 4C1 = 4ways
A large package can have 3 notepads of different colors in 4C3 ways = 4
A large package can have 3 notepads of same color in 4C1 = 4ways

So, total number of packages is 4+4+4+4 = 16

Hence, C
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by cans » Fri Jun 03, 2011 10:51 am
2 sizes - s1,s2
colors-b,g,y,p
package = same size and same color + same size different color.
same size, same color - 2C1*4C1 = 8 ( one of the 2 sizes and one of the 4 colors)
same size, different color - 2C1*4C3 = 8 ( one of the 2 sizes and 3 of the 4 colors)
Total = 16
IMO C
Assumption: When it says different, all 3 colors are different
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