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

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A certain office supply store stocks 2 sizes of self-stick n [#permalink] New post 04 Nov 2009, 19:27
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Question Stats:

74% (02:07) correct 26% (00:47) wrong based on 51 sessions
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 pacakages 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

OPEN DISCUSSION OF THIS QUESTION IS HERE: a-certain-office-supply-store-stocks-2-sizes-of-self-stick-92842.html
[Reveal] Spoiler: OA

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Last edited by Bunuel on 23 Oct 2013, 00:53, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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Director
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Re: sticky pads [#permalink] New post 04 Nov 2009, 19:27
completly confused with so much of info..

Ok so lets say two sizes: small and large:
Each has B,G,Y,P colors.

We need case1 + case2
case1:same size same color
case2:same size diff. color

case1:
same size:Out of 2 we select 1: 2C1
same color: 4 ways either all B,all G,all Y..etc : 4
therefore case 1 gives us 8.

Case2:
same size:2C1
diff. color..hmmmm

Numerator:there are three slots,in first slot all 4 coors poss,in second slot 3 colors poss,in third slot 2 colors poss..therefore: 4!

Denominator:4 x 4 x 4

ok.ugly result..Help!Where am i gong wrong?
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Re: sticky pads [#permalink] New post 04 Nov 2009, 19:39
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tejal777 wrote:
2 sizes of sticky pads. Each has 4 colors - Blue, Green, Yellow, and Purple. The pads are packed in packages that contain either 3 notepads of same size and same color or 3 notepads of same size and of 3 different colors. How many different packages of the types described are possible?
a. 6
b. 8
c. 16
d. 24
e. 32


Okay, calm down tejal... keeping head cool is the key... This problem is very easy if you employ the correct approach and here is the right one:

Packages can be prepared in following 2 ways:
1) 3 notepads of same size and same color
2) 3 notepads of same size and of 3 different colors

Lets go step by step.
1) 3 notepads of same size and same color:
We know that there are 2 sizes of pads and 4 colors in total. We want to keep the size and color same. so there are 2*4 = 8 ways to create package.

2) 3 notepads of same size and of 3 different colors:
We want to select 3 colors out of 4 available = 4C3 = 4
And there are 2 sizes of notepad available. So the total ways in which a package can be created is = 4C3*2 = 8

So total 8+8 = 16 packages can be created. Answer is C.

Questions? Bring them on :)

Last edited by hgp2k on 04 Nov 2009, 19:41, edited 1 time in total.
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Re: sticky pads [#permalink] New post 04 Nov 2009, 19:39
tejal777 wrote:
2 sizes of sticky pads. Each has 4 colors - Blue, Green, Yellow, and Purple. The pads are packed in packages that contain either 3 notepads of same size and same color or 3 notepads of same size and of 3 different colors. How many different packages of the types described are possible?
a. 6
b. 8
c. 16
d. 24
e. 32


Sizes: small and large
Colors: B, G, Y, P

Case 1: 3 the same size and 3 the same color
2 sizes x 4 colors = 8 total

Case 2: There are four colors but we are to choose three. 4C3 = 4 X 2 (because two sizes) = 8

Total = 16
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Re: sticky pads [#permalink] New post 04 Nov 2009, 19:41
tejal777 wrote:

Case2:
same size:2C1
diff. color..hmmmm

Numerator:there are three slots,in first slot all 4 coors poss,in second slot 3 colors poss,in third slot 2 colors poss..therefore: 4!

Denominator:4 x 4 x 4

ok.ugly result..Help!Where am i gong wrong?


The problem is that you didn't get the combinations of colors but rather the combinations of sizes
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Re: sticky pads [#permalink] New post 23 Oct 2013, 00:45
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Re: A certain office supply store stocks 2 sizes of self-stick n [#permalink] New post 23 Oct 2013, 00:54
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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

Notepads of the same color = 4 (we have 4 colors). As we have two sizes then total for the same color=4*2=8

Notepads of the different colors = 4C3=4 (we should choose 3 different colors out of 4). As we have two sizes then total for the different color=4*2=8

Total=8+8=16

Answer: C.

OPEN DISCUSSION OF THIS QUESTION IS HERE: a-certain-office-supply-store-stocks-2-sizes-of-self-stick-92842.html
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Re: A certain office supply store stocks 2 sizes of self-stick n   [#permalink] 23 Oct 2013, 00:54
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