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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]

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17 Apr 2010, 10:05
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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 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
[Reveal] Spoiler: OA
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17 Apr 2010, 10:26
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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

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22 Dec 2010, 08:08
bunuel can you make me more clear, how it is 4 books of same colour

thank u
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22 Dec 2010, 08:20
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anilnandyala wrote:
bunuel can you make me more clear, how it is 4 books of same colour

thank u

Sure.

As the pads are packed in packages that contain only the notepads of same size then let's calculate for one size and then multiply it by 2 to get total.

There are 4 colors so there are 4 different packages possible with 3 same color notepads: all 3 Blue, all 3 Green, all 3 Yellow, or all 3 Purple;

For 3 different color pads: again as there are 4 colors then 4C3=4 is the # of ways to choose 3 different color pads to make a package: {BGY}, {BGP}, {BYP}, {GYP};

So for one size there are 4+4=8 packages possible thus for 2 sizes there are 8*2=16 packages possible.

Hope it's clear.
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08 Jan 2012, 15:33
You have 2 sizes and 4 colors (Call them A,B,C,D) to do this problem you should consider that for each size you can have 2 types of package call them type X and type y

Type X is of all the same color so for size 1 type X is

A
B
C
D

Type Y is of all the different colors for size 1 type Y is all the ways you can have 3 of ABCD

You could say that you are choosing 3 of the 4 colors for each package therefore this is

4C3=4
or you could list them out working as if ABCD are in a circle and you want to list them moving only one letter into and out of your arrangement at a time.

ABC
BCD
CDA
DAB
so either way you see 4 ways for Type Y

Since you have 2 sizes and 8 ways to arrange each size you have a total of 16 packages.

Hope this helped
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08 Jan 2012, 20:24
Too big a question for too small an answer...

2 sizes of B, G, Y and P

1. Same size, same color = 1st size same color (4) and 2nd size same color (4) = 8
2. Same size, diff color = 1st size diff color 4!/3!1! = 4, same for second size = 8

Together = 16
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09 Jan 2012, 19:29
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Kotela,

Sorry if I was not clear. I generally keep my answers short.

There are two ways this can happen.:

1. Same size same color:
There are eight such combinations
size 1
1-BBB
1-GGG
1-YYY
1-PPP
size 2
2-BBB
2-GGG
2-YYY
2-PPP

total 8

2. Same size different color
size 1
4C3 = 4 (BGY, BYP, GYP, BGP)
size 2
4C3 = 4 (same as above)
Total 8

Notice there there is an OR in the stem, so add
8 + 8 = 16

Hope this helps!
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09 Jan 2012, 19:44
shinbhu wrote:
Kotela,

Sorry if I was not clear. I generally keep my answers short.

There are two ways this can happen.:

1. Same size same color:
There are eight such combinations
size 1
1-BBB
1-GGG
1-YYY
1-PPP
size 2
2-BBB
2-GGG
2-YYY
2-PPP

total 8

2. Same size different color
size 1
4C3 = 4 (BGY, BYP, GYP, BGP)
size 2
4C3 = 4 (same as above)
Total 8

Notice there there is an OR in the stem, so add
8 + 8 = 16

Hope this helps!

Simply superb..................

Thanks a lot for the explanation

+1 Kudos for you
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Re: A certain office supply store stocks 2 sizes of self-stick [#permalink]

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05 Dec 2013, 16:16
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Re: A certain office supply store stocks 2 sizes of self-stick [#permalink]

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30 Dec 2013, 07:26
msand 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 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

First scenario 2C1 * 4C3 = 8
Second scenario 2C1*4C1 = 8

Total 16

Hope it helps
Cheers!
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Re: A certain office supply store stocks 2 sizes of self-stick [#permalink]

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02 Jan 2015, 10:54
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Re: A certain office supply store stocks 2 sizes of self-stick [#permalink]

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09 Feb 2016, 05:17
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Re: A certain office supply store stocks 2 sizes of self-stick [#permalink]

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12 Feb 2016, 18:35
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Hi All,

The question is essentially about the Combination Formula and following instructions. However, if you don't realize that, then you can always "brute force" the solution - you just have to draw it all out.

We're told that there are 2 sizes of notepads and 4 colors (Blue, Green, Yellow, Prink) of notepads. For organizational purposes, I'm going to refer to the 8 types of pads as:

Etc.

Now, we just need to figure out how many options fit each description:

1st: 3 notepads of the SAME SIZE and SAME COLOR….

BBB
bbb
GGG
ggg
YYY
yyy
PPP
ppp

8 options

2nd: 3 notepads of the SAME SIZE and 3 DIFFERENT COLORS

BGY
BGP
BYP
GYP
bgy
bgp
byp
gyp

8 options

Total options = 8 + 8 = 16

[Reveal] Spoiler:
C

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Re: A certain office supply store stocks 2 sizes of self-stick [#permalink]

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09 Apr 2016, 14:10
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msand 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 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

we have 2 types of notebooks.
we can select either 3 colors or 1 color
to select 3 colors: 4C3 = 4
to select 1 color: 4C1 = 4
so for each type of notebook, we have 8 possible arrangements
8x2 = 16

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Re: A certain office supply store stocks 2 sizes of self-stick [#permalink]

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27 Apr 2017, 08:43
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Re: A certain office supply store stocks 2 sizes of self-stick [#permalink]

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11 May 2017, 21:35
Effectively, selecting 1 out of 4 (colors) is same as 3 out of 4
as 1C4 = 3C4 = 4

And selecting 1 out of 2 sizes = 2

Hence, Packet Type 1 = Packet Type 2 = 4 x 2 = 8
And hence the total type = type1 + type2 = 8 + 8 = 16

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Re: A certain office supply store stocks 2 sizes of self-stick [#permalink]

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11 May 2017, 23:14
msand 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 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

There are 2 sizes of self stick notepads.
Also available colors are 4 : Blue, Green, Yellow, Pink.

Case 1: The packages can be of 3 notepads of the same size and the same color
1st size : No. of packages possible : 4C1 = 4
2nd size: No. of packages possible = 4C1 = 4

Case 2: The packages can be of 3 notepads of the same size and of 3 different colors
1st size : No. of packages possible : 4C3 = 4
2nd size : No. of packages possible : 4C3 = 4

Total no. of different packages possible if order in which colors are packed is not considered : (4+4)+(4+4) = 16
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Re: A certain office supply store stocks 2 sizes of self-stick [#permalink]

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20 May 2017, 19:56
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msand 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 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

1. Ordering is not important, so this is a combination problem
2. Is there a constraint? There are two cases each with a constraint
3. In the first case ,Constraint is 3 notebooks of the same color . So there are 2 ways of selecting a size and 4C1 ways of selecting a color. So a total of 2*4= 8 ways
4. In the second case, constraint is 3 notebooks of the same size but 3 different colors. There are 2 ways of selecting a size and 4C3 ways of selecting colors, for a total of 2*4=8 ways
5. Total number of combinations is (3) + (4) = 16
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Re: A certain office supply store stocks 2 sizes of self-stick   [#permalink] 20 May 2017, 19:56
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