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Bunuel
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Andrew is trying to organize his notes by subject with a color-coding 21 Mar 2017, 04:45
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D
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25% (medium)

Question Stats:

74% (01:11) correct 26% (01:22) wrong based on 310 sessions

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Andrew is trying to organize his notes by subject with a color-coding system. If he has 5 different colors to work with, and a code can consist of one or two colors, how many subjects can he organize with this system if the order of the colors doesn’t matter?

A. 5
B. 7
C. 10
D. 15
E. 25
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D
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Andrew is trying to organize his notes by subject with a color-coding Updated on: 21 Mar 2017, 12:05
Originally posted by BrentGMATPrepNow on 21 Mar 2017, 08:26.
Last edited by BrentGMATPrepNow on 21 Mar 2017, 12:05, edited 1 time in total.
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Bunuel
Andrew is trying to organize his notes by subject with a color-coding system. If he has 5 different colors to work with, and a code can consist of one or two colors, how many subjects can he organize with this system if the order of the colors doesn’t matter?

A. 5
B. 7
C. 10
D. 15
E. 25
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Codes consisting of 1 color
There are 5 colors to choose from, so there are 5 codes consisting of 1 color

Codes consisting of 2 colors
Since order doesn't matter (e.g., selecting blue then red is the same as selecting red then blue), we can use combinations.
We can select 2 colors from 5 colors in 5C2 ways (= 10 ways)
So there are 10 codes consisting of 2 colors

TOTAL = 5 + 10
= 15

Answer:
Show Spoiler
C

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Andrew is trying to organize his notes by subject with a color-coding 21 Mar 2017, 09:31
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Bunuel
Andrew is trying to organize his notes by subject with a color-coding system. If he has 5 different colors to work with, and a code can consist of one or two colors, how many subjects can he organize with this system if the order of the colors doesn’t matter?

A. 5
B. 7
C. 10
D. 15
E. 25

Codes consisting of 1 color
There are 5 colors to choose from, so there are 5 codes consisting of 1 color

Codes consisting of 2 colors
Since order doesn't matter (e.g., selecting blue then red is the same as selecting red then blue), we can use combinations.
We can select 2 colors from 5 colors in 5C2 ways (= 10 ways)
So there are 10 codes consisting of 2 colors

TOTAL = 5 + 10
= 10

Answer:
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C

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Please edit the answer. 5+10=15. Hence D.

Cheers!
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Andrew is trying to organize his notes by subject with a color-coding 21 Mar 2017, 12:06
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Diwakar003


Please edit the answer. 5+10=15. Hence D.

Cheers!
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Let me check my calculator . . . nerts!!!

Thanks for the heads up!! :-D

Cheers,
Brent
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Andrew is trying to organize his notes by subject with a color-coding 21 Mar 2017, 19:55
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Bunuel
Andrew is trying to organize his notes by subject with a color-coding system. If he has 5 different colors to work with, and a code can consist of one or two colors, how many subjects can he organize with this system if the order of the colors doesn’t matter?

A. 5
B. 7
C. 10
D. 15
E. 25
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Total number of color codes that can be created using 5 colors would be - \(5C1\) + \(5C2\)
=\(5 + 10\) = 15.

D.
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Andrew is trying to organize his notes by subject with a color-coding 23 Mar 2017, 17:02
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Bunuel
Andrew is trying to organize his notes by subject with a color-coding system. If he has 5 different colors to work with, and a code can consist of one or two colors, how many subjects can he organize with this system if the order of the colors doesn’t matter?

A. 5
B. 7
C. 10
D. 15
E. 25
Show more

Let’s say the 5 colors are as follows: A, B, C, D, and E. He can have the following codes:

A, AB, AC, AD, AE

B, BC, BD, BE

C, CD, CE

D, DE

E

Alternate Solution:

Since Andrew can select either 1 or 2 colors from the 5, he can create the following number of codes:

5C2 + 5C1 = (5 x 3)/2! + 5 = 10 + 5 = 15

Answer: D
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Andrew is trying to organize his notes by subject with a color-coding 24 Mar 2017, 13:19
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Since the order doesn't matter in this case, combinations should be used.
5C1 + 5C2
5!/(5-1)!1! + 5!/(5-2)!2!
5x4!/4!1! + 5x4x3!/3!2!
5 + 10
15

Which is answer D
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Andrew is trying to organize his notes by subject with a color-coding 05 Jun 2024, 03:02
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