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

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Math Expert
Joined: 02 Sep 2009
Posts: 58464

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27 Feb 2019, 23:25
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Difficulty:

15% (low)

Question Stats:

86% (02:21) correct 14% (02:42) wrong based on 35 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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Joined: 18 Aug 2017
Posts: 5043
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)

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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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Joined: 24 Feb 2019
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Location: Brazil
Concentration: Strategy, General Management
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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)?

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Joined: 18 Aug 2017
Posts: 5043
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)

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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)?

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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Joined: 24 Feb 2019
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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)?

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.
Re: Sandy is designing an Internet banner advertisement and has decided to   [#permalink] 01 Mar 2019, 08:57
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