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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 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

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.

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.

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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DS - If negative answer only, still sufficient. No need to find exact solution. PS - Always look at the answers first CR - Read the question stem first, hunt for conclusion SC - Meaning first, Grammar second RC - Mentally connect paragraphs as you proceed. Short = 2min, Long = 3-4 min

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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I am the master of my fate. I am the captain of my soul. Please consider giving +1 Kudos if deserved!

DS - If negative answer only, still sufficient. No need to find exact solution. PS - Always look at the answers first CR - Read the question stem first, hunt for conclusion SC - Meaning first, Grammar second RC - Mentally connect paragraphs as you proceed. Short = 2min, Long = 3-4 min

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

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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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:

B = Big blue pad b = Little blue pad G = Big green pad g = LIttle green pad 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

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

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, 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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