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A certain office supply store stocks 2 sizes of selfstick
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17 Apr 2010, 10:05
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A certain office supply store stocks 2 sizes of selfstick 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
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Re: colors and size of pads
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17 Apr 2010, 10:26
A certain office supply store stocks 2 sizes of selfstick 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.
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Re: Permutations and combinations
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09 Jan 2012, 19:29
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 1BBB 1GGG 1YYY 1PPP size 2 2BBB 2GGG 2YYY 2PPP 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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Re: colors and size of pads
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22 Dec 2010, 08:08
bunuel can you make me more clear, how it is 4 books of same colour
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Re: colors and size of pads
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22 Dec 2010, 08:20
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.
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Re: Permutations and combinations
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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.
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Re: Permutations and combinations
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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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Re: A certain office supply store stocks 2 sizes of selfstick
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30 Dec 2013, 07:26
msand wrote: A certain office supply store stocks 2 sizes of selfstick 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 Hence, answer is C Hope it helps Cheers! J



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Re: A certain office supply store stocks 2 sizes of selfstick
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12 Feb 2016, 18:35
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 BGY BGP BYP GYP bgy bgp byp gyp 8 options Total options = 8 + 8 = 16 Final Answer: GMAT assassins aren't born, they're made, Rich
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Re: A certain office supply store stocks 2 sizes of selfstick
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09 Apr 2016, 14:10
msand wrote: A certain office supply store stocks 2 sizes of selfstick 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 C



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Re: A certain office supply store stocks 2 sizes of selfstick
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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 Hit Kudos if you like the response !!!
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Re: A certain office supply store stocks 2 sizes of selfstick
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11 May 2017, 23:14
msand wrote: A certain office supply store stocks 2 sizes of selfstick 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 selfstick
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20 May 2017, 19:56
msand wrote: A certain office supply store stocks 2 sizes of selfstick 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 selfstick
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19 Apr 2018, 18:03
msand wrote: A certain office supply store stocks 2 sizes of selfstick 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. Answer: C
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Re: A certain office supply store stocks 2 sizes of selfstick
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02 Jun 2018, 17:53
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 Pls explain..what am I missing here? Thanks In advance Regards



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Re: A certain office supply store stocks 2 sizes of selfstick
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03 Jun 2018, 04:58
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 selfstick 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
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Re: A certain office supply store stocks 2 sizes of selfstick
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26 Aug 2018, 18:46
Hello,
What if there where 5 colours total.



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Re: A certain office supply store stocks 2 sizes of selfstick
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27 Aug 2018, 11:18
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?)? GMAT assassins aren't born, they're made, Rich
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Re: A certain office supply store stocks 2 sizes of selfstick
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21 Dec 2018, 10:17
A certain office supply store stocks 2 sizes of selfstick 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[/quote]
Shouldn't this be:
For large size.. 3 Blue 3 Green 3 Yellow 3 Pink
For small size.. 3 Blue 3 Green 3 Yellow 3 Pink



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Re: A certain office supply store stocks 2 sizes of selfstick
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29 Sep 2019, 14:06
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. GMAT assassins aren't born, they're made, Rich
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Re: A certain office supply store stocks 2 sizes of selfstick
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