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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?
Re: A certain office supply store stocks 2 sizes of self-stick notepads
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17 Apr 2010, 09:26
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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
Re: A certain office supply store stocks 2 sizes of self-stick notepads
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22 Dec 2010, 07:20
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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.
Re: A certain office supply store stocks 2 sizes of self-stick notepads
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30 Dec 2013, 06:26
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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
First scenario 2C1 * 4C3 = 8 Second scenario 2C1*4C1 = 8
Re: A certain office supply store stocks 2 sizes of self-stick notepads
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12 Feb 2016, 17:35
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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:
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 notepads
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09 Apr 2016, 13:10
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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 notepads
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20 May 2017, 18:56
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Top Contributor
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 _________________
Re: A certain office supply store stocks 2 sizes of self-stick notepads
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19 Apr 2018, 17:03
Expert Reply
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
Let’s say the 2 sizes of notepads are small and large. Then, for the small notepads, there are 4 packages of notepads of all the same color (one package for each color) and 4C3 = 4 packages of notepads of three different colors. Thus, for the small notepads, there are a total of 4 + 4 = 8 different packages. Similarly, there are 8 different packages for the large notepads. Thus, there are a total of 8 + 8 = 16 different packages for the 2 sizes of notepads.
Re: A certain office supply store stocks 2 sizes of self-stick notepads
[#permalink]
02 Jun 2018, 16:53
Bunuel wrote:
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.
Answer: C.
Hope it's clear.
Hi Bunuel,
Sorry but I don't follow this..
When there are 4 colors and 2 sizes there are total of only 8 notepads..how can we have 3 blue. 3 green 3 yellow and 3 purple
Re: A certain office supply store stocks 2 sizes of self-stick notepads
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03 Jun 2018, 03:58
Expert Reply
zanaik89 wrote:
Bunuel wrote:
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.
Answer: C.
Hope it's clear.
Hi Bunuel,
Sorry but I don't follow this..
When there are 4 colors and 2 sizes there are total of only 8 notepads..how can we have 3 blue. 3 green 3 yellow and 3 purple
Pls explain..what am I missing here?
Thanks In advance
Regards
A certain office supply store stocks 2 sizes of self-stick notepads, each in 4 colors: Blue, Green, Yellow Or Pink. So, we have:
Large size notepads: 4 BLUE 4 GREEN 4 YELLOW 4 PINK
Small size notepads 4 blue 4 green 4 yellow 4 pink _________________
Re: A certain office supply store stocks 2 sizes of self-stick notepads
[#permalink]
27 Aug 2018, 10:18
Expert Reply
Hi andresan,
Even if there were 5 colors (instead of 4), the approaches would not change - you can either use the Combination formula or 'brute force' the list of options. Have you attempted either approach (and what answer did you get?)?
Re: A certain office supply store stocks 2 sizes of self-stick notepads
[#permalink]
29 Sep 2019, 13:06
Expert Reply
Hi ishaan100,
The numbers "4" and "3" have specific meanings in the context of this question - and do NOT refer to the total number of notepads in the store.
1) There are 4 different colors of pad: Blue, Green, Yellow and Pink - and each color appears in 2 different sizes. 2) Each package contains 3 types of pads: either all the same size & color OR the same size & 3 different colors.
Most of the posts in this thread define how there are 16 POSSIBLE packages of notepads - but again, that has nothing to do with the actual number of notepads in the store.
I am just starting on P&C so I too struggle with it. Therefore, I want to ask something about this question. I have gone through all the solutions provided on this thread but I am not being able to clear my head about something. How did we take into account that fact that we have to make 3 notepads.
We have to make either 3 notepads of the same size and the same color or 3 notepads of the same size and of 3 different colors right? 3 notepads of the same size and the same color + 3 notepads of the same size and of 3 different colors right Choose 1 size out of 2 and Choose 1 color out of 4 + Choose 1 size out of 2 and Choose 1 color out of 4 2C1 * 4C1 + 2C1 * 4C3 = 16 I understood this but how did me make 3 notepads though ?
Thank you, Dablu
Originally posted by gurudabl on 08 Mar 2020, 21:43.
Last edited by gurudabl on 15 May 2020, 22:17, edited 2 times in total.
Re: A certain office supply store stocks 2 sizes of self-stick notepads
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15 May 2020, 06:55
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Top Contributor
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 two different cases to consider: 1) All 3 pads the same color 2) The 3 pads are 3 different colors
Case 1: All 3 pads the same color Take the task of packaging pads and break it into stages.
Stage 1: Select a size There are 2 possible sizes, so we can complete stage 1 in 2 ways.
Stage 2: Select 1 color (to be applied to all 3 pads) There are 4 possible colors from which to choose, so we can complete stage 2 in 4 ways.
By the Fundamental Counting Principle (FCP) we can complete the two stages in (2)(4) ways (= 8 ways)
Case 2: The 3 pads are 3 different colors Take the task of packaging pads and break it into stages.
Stage 1: Select a size There are 2 possible sizes, so we can complete stage 1 in 2 ways.
Stage 2: Select 3 different colors There are 4 possible colors, and we must choose 3 of them. Since the order of the selected colors does not matter, we can use combinations. We can select 3 colors from 4 colors in 4C3 ways (4 ways), so we can complete stage 2 in 4 ways.
By the Fundamental Counting Principle (FCP) we can complete the two stages in (2)(4) ways (= 8 ways)
So, both cases can be completed in a total of 8 + 8 ways = 16
Answer: C
Note: the FCP can be used to solve the MAJORITY of counting questions on the GMAT. So, be sure to learn it.
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