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A certain office supply store stocks 2 sizes of self-stick

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A certain office supply store stocks 2 sizes of self-stick [#permalink] New post 23 Oct 2005, 17:09
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 and 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: GMATPrep - Combinations [#permalink] New post 23 Oct 2005, 18:00
rigger wrote:
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 and 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


Is it 2 C 1 * 4 C 1 + 2 C 1 * 4 C 3 = 24

(ether size and one color out of 4 ) or (either size and 3 colors out of 4)
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 [#permalink] New post 23 Oct 2005, 19:06
The answer is indeed C (16).

Same size and same color + same size & different color
-> same size = 2C1
-> same color = 4C1
-> diff color = 4C3
Since, 4C1 = 4C3.

Answer = 2 * (2C1 * 4C1) = 2 * 2 * 4 = 16.
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 [#permalink] New post 23 Oct 2005, 19:43
rigger wrote:
The OA is 16 or (c).


I got the same reasoning but goofed on maths, it wont cut it at the test.
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 [#permalink] New post 23 Oct 2005, 20:42
Hi,

Can you explained how you can up with the combinations?

Cheers,
Rigger
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 [#permalink] New post 23 Oct 2005, 21:18
I am explaning only part of the problem. Hope you can co-relate and understand the complete one.

The question provides 4 different colors and asks for how many types are possible with same color or different color. The question did not ask for the 'order' or 'sequence' of colors. Hence the combination is chosen. If the question asks for order or sequence, then a permutation should be chosen.

Choosing same color is equal to choosing 1 color out of 4. Choosing different color is equal to choosing 3 color out of 4.

Hope this helps. Pls post back if you have more questions.
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 [#permalink] New post 24 Oct 2005, 00:53
Chose 3 colors from a set of 4: 4c3 = 4
Add Uniform colors packages: +4 (because we have 4 colors)
Each package can be small or large (or whatever the sizes are, but they are two different ones)

8 x 2 = 16
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Re: GMATPrep - Combinations [#permalink] New post 24 Oct 2005, 01:29
rigger wrote:
The store packs the notepads in packages that contain either 3 notepads of the same size and the same color or 3 notepads of the same size and of 3 different colors.


how is it possible to pack 3 notepads of the same color. i mean there are only 2 notepads that have the same colour:

1st size: bgyp 2nd size: bgyp

is it or am i missing something ?
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Re: GMATPrep - Combinations [#permalink] New post 24 Oct 2005, 02:06
christoph wrote:
rigger wrote:
The store packs the notepads in packages that contain either 3 notepads of the same size and the same color or 3 notepads of the same size and of 3 different colors.


how is it possible to pack 3 notepads of the same color. i mean there are only 2 notepads that have the same colour:

1st size: bgyp 2nd size: bgyp

is it or am i missing something ?


ich glaub du hast da was missverstanden :P

package same color 1st size= bbb
package same color 2nd size = bbb

oder drei andersfarbige jeweils in zwei größen

package different color 1st size = bgy
package different color 2nd size = bgy
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Re: GMATPrep - Combinations [#permalink] New post 24 Oct 2005, 05:36
nero44 wrote:
christoph wrote:
rigger wrote:
The store packs the notepads in packages that contain either 3 notepads of the same size and the same color or 3 notepads of the same size and of 3 different colors.


how is it possible to pack 3 notepads of the same color. i mean there are only 2 notepads that have the same colour:

1st size: bgyp 2nd size: bgyp

is it or am i missing something ?


ich glaub du hast da was missverstanden :P

package same color 1st size= bbb
package same color 2nd size = bbb

oder drei andersfarbige jeweils in zwei größen

package different color 1st size = bgy
package different color 2nd size = bgy


ah ja. woher kommst du ?
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Re: GMATPrep - Combinations [#permalink] New post 24 Oct 2005, 09:13
christoph wrote:
nero44 wrote:
christoph wrote:
rigger wrote:
The store packs the notepads in packages that contain either 3 notepads of the same size and the same color or 3 notepads of the same size and of 3 different colors.


how is it possible to pack 3 notepads of the same color. i mean there are only 2 notepads that have the same colour:

1st size: bgyp 2nd size: bgyp

is it or am i missing something ?


ich glaub du hast da was missverstanden :P

package same color 1st size= bbb
package same color 2nd size = bbb

oder drei andersfarbige jeweils in zwei größen

package different color 1st size = bgy
package different color 2nd size = bgy


ah ja. woher kommst du ?


Köln, du? test schon genommen?
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Re: GMATPrep - Combinations [#permalink] New post 24 Oct 2005, 09:19
nero44 wrote:

Köln, du? test schon genommen?


frankfurt...muss wiederholen...nächste woche und du ?
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Re: GMATPrep - Combinations [#permalink] New post 24 Oct 2005, 09:23
christoph wrote:
nero44 wrote:

Köln, du? test schon genommen?


frankfurt...muss wiederholen...nächste woche und du ?


auch zweite runde :) hatte 640 im ersten q44 und v34 oder so...
ich weiss nich ob ich den noch im oktober machen soll oder nicht, da ich im nov nich soviel zeit hab.
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 [#permalink] New post 24 Oct 2005, 15:14
Oh my, I feel so lucky that GMAT doesn't test foreign language abilities. ;)
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 [#permalink] New post 24 Oct 2005, 15:28
HongHu wrote:
Oh my, I feel so lucky that GMAT doesn't test foreign language abilities. ;)


Looks like nero44 met a relative here :)
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 [#permalink] New post 03 Jan 2006, 00:01
sehr gut nero und christoph. Ich kommst muenchen aus.
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 [#permalink] New post 03 Jan 2006, 08:53
Assume the 2 sizes are large and small. So we have larg

Case 1: Same size, same color
Case 2: Same size, different color

We're told order doesn't matter, so combinations is to be used (actually, we're picking a group of 3 objects, so arrangement doesn't matter even if we're not told)

Assume the two sizes are large and small.
Then, large blue pads would be denoted by lb, large green pads by lg, large yellow pads by ly and large pink pads by lp. Small pads would be denoted the same way replacing l with s.

Case 1: 3 pads of the same size and same color
- Possibilties, (lb, lb, lb), (lp, lp, lp), (lg, lg, lg), (lp, lp, lp) and another set with small pads.
- # of ways = 8

Case 2: 3 pads of the same size but different color
- # of ways = # of ways to pick 3 colors from 4 colors (large size) + # of ways to pick 3 colors from 4 colors (small size) = 4C3 * 2 = 8

Total number of ways = 16

Ans C
  [#permalink] 03 Jan 2006, 08:53
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