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A certain office supply store stocks 2 sizes of self-stick [#permalink]
 17 Apr 2010, 10:05
Question Stats:
78% (02:24) correct
21% (01:08) wrong based on 1 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
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Re: colors and size of pads [#permalink]
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 Answer: C.
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Re: colors and size of pads [#permalink]
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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Re: colors and size of pads [#permalink]
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. Answer: C. Hope it's clear.
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Permutations and combinations [#permalink]
08 Jan 2012, 03:11
Can anyone please help me in solving this problem.......
Attachments
Number1.jpg [ 66.23 KiB | Viewed 1554 times ]
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Re: Permutations and combinations [#permalink]
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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Re: Permutations and combinations [#permalink]
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: Permutations and combinations [#permalink]
09 Jan 2012, 18:18
Dude.....i am not clear with this......can you elaborate a bit more please.....
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Re: Permutations and combinations [#permalink]
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 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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Re: Permutations and combinations [#permalink]
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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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
Thanks
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