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Sandy is designing an Internet banner advertisement and has decided to

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Sandy is designing an Internet banner advertisement and has decided to  [#permalink]

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New post 27 Feb 2019, 23:25
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Question Stats:

90% (02:15) correct 10% (02:58) wrong based on 20 sessions

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Sandy is designing an Internet banner advertisement and has decided to use one background, one font, two different accent images, and four different colors. If Sandy has 5 backgrounds, 4 fonts, 6 accent images, and 12 colors from which to choose, then how many different banners can she make?

A. 148,500
B. 49,500
C. 37,125
D. 29,700
E. 24,750

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Re: Sandy is designing an Internet banner advertisement and has decided to  [#permalink]

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New post 28 Feb 2019, 05:03
Bunuel wrote:
Sandy is designing an Internet banner advertisement and has decided to use one background, one font, two different accent images, and four different colors. If Sandy has 5 backgrounds, 4 fonts, 6 accent images, and 12 colors from which to choose, then how many different banners can she make?

A. 148,500
B. 49,500
C. 37,125
D. 29,700
E. 24,750



5c1*4c1*6c2*12c4
148500
IMO A
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Re: Sandy is designing an Internet banner advertisement and has decided to  [#permalink]

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New post 28 Feb 2019, 22:56
Why doesn't the order of the colors and images matter, in this case? I considered that if Sandy chooses for instance red for the left part and blue for the right part of the banner, those would be two different banners - and for this reason I calculated using permutation and not combination.

Which part of the problem statement would hint this to me (instead of calculating everything and then noticing that the number I got is not one of the possible answers)?

Thanks in advance!
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Re: Sandy is designing an Internet banner advertisement and has decided to  [#permalink]

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New post 28 Feb 2019, 23:00
FTGreco wrote:
Why doesn't the order of the colors and images matter, in this case? I considered that if Sandy chooses for instance red for the left part and blue for the right part of the banner, those would be two different banners - and for this reason I calculated using permutation and not combination.

Which part of the problem statement would hint this to me (instead of calculating everything and then noticing that the number I got is not one of the possible answers)?

Thanks in advance!

FTGreco

Please share the formula you tried using

Apply the combinatorics formula to detetmine the possible options Sandy can choose from to get what he desires..
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Re: Sandy is designing an Internet banner advertisement and has decided to  [#permalink]

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New post 01 Mar 2019, 08:57
Archit3110 wrote:
FTGreco wrote:
Why doesn't the order of the colors and images matter, in this case? I considered that if Sandy chooses for instance red for the left part and blue for the right part of the banner, those would be two different banners - and for this reason I calculated using permutation and not combination.

Which part of the problem statement would hint this to me (instead of calculating everything and then noticing that the number I got is not one of the possible answers)?

Thanks in advance!


Please share the formula you tried using

Apply the combinatorics formula to detetmine the possible options Sandy can choose from to get what he desires..


Okay, so the way I originally did this was by considering that she will use 1 Background (B, with 5 different options), 1 Font (F, with 4 different options), 2 Accent images (A1 with 6 different options and A2 with 5 remaining different options), and 4 Colors (C1, C2, C3, C4 with 12, 11, 10, 9 possible options respectively) to create a banner, resulting in 5*4*(6*5)*(12*11*10*9) = 7,128,000.

This is the same as simply applying the formula 5P1 * 4P1 * 6P2 * 12P4 = 7,128,000 which is not listed as a possible answer, since this method assumes that the order matters (so choosing red to paint one part and then blue to paint another part of the banner is different from using blue and then red).

I now understand what is the right way to solve this question (using combinations and not permutations), but I'd like to know if there is one key part of the problem statement that could indicate to me whether the order of the chosen elements (e.g. red and blue vs blue and red) should make a difference or not.
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Re: Sandy is designing an Internet banner advertisement and has decided to   [#permalink] 01 Mar 2019, 08:57
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