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At a certain laboratory, chemical substance are identified by an unord

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At a certain laboratory, chemical substance are identified by an unord [#permalink]

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New post 04 Jan 2015, 09:22
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At a certain laboratory, chemical substance are identified by an unordered combination of three different colors. If no chemical may be assigned the same three colors as any other, what is the maximum number of substances that can be identified using seven colors?

A) 21
B) 35
C) 105
D) 135
E) 210

Looking for easier method to solve this.
[Reveal] Spoiler: OA

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Re: At a certain laboratory, chemical substance are identified by an unord [#permalink]

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New post 04 Jan 2015, 09:59
Since no chemical may be assigned the same three colors as any other. So order does matter. So answer should be 7C3 = 35 ?
amidamani13 wrote:
Solve:

At a certain laboratory, chemical substance are identified by an unordered combination of three different colors. If no chemical may be assigned the same three colors as any other, what is the maximum number of substances that can be identified using seven colors?

A) 21
B) 35
C) 105
D) 135
E) 210

Looking for easier method to solve this.

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Re: At a certain laboratory, chemical substance are identified by an unord [#permalink]

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New post 04 Jan 2015, 11:23
Hi amidamani13,

You mentioned in your post that you were looking for an "easier" method to solve this problem. What method were using before (or what method did the explanation that came with this question use?)?

"Combination" questions are a rarer category on Test Day (you'll see 1, but you might see 1-2 more). In this prompt, the words "unordered" and "combinations" provide the clues to let you know that you can use the Combination Formula to answer the question.

Combinations = N!/[K!(N-K)!] where N is the total number of items and K is the size of the subgroup

Here, we have 7 colors and we're choosing combinations of 3. Plugging those values in, we get...

7!/(3!4!) = (7)(6)(5)/(3)(2)(1) = (7)(5) = 35 combinations of 3 colors.

Final Answer:
[Reveal] Spoiler:
B


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Re: At a certain laboratory, chemical substance are identified by an unord [#permalink]

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New post 05 Jan 2015, 01:49
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amidamani13 wrote:
At a certain laboratory, chemical substance are identified by an unordered combination of three different colors. If no chemical may be assigned the same three colors as any other, what is the maximum number of substances that can be identified using seven colors?

A) 21
B) 35
C) 105
D) 135
E) 210

Looking for easier method to solve this.


Check Constructing Numbers, Codes and Passwords in our Special Questions Directory.
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Re: At a certain laboratory, chemical substance are identified by an unord [#permalink]

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New post 15 Jan 2016, 19:52
Bunuel wrote:
amidamani13 wrote:
At a certain laboratory, chemical substance are identified by an unordered combination of three different colors. If no chemical may be assigned the same three colors as any other, what is the maximum number of substances that can be identified using seven colors?

A) 21
B) 35
C) 105
D) 135
E) 210

Looking for easier method to solve this.


Check Constructing Numbers, Codes and Passwords in our Special Questions Directory.


Hello Bunuel,

Since the question says it is unordered and no chemical can have same 3 colors -> This should not omit the possibility of 2 same colors in 3 color combination right?
I was looking for an option which has 7*7*5 maximum number of substances.
Isn't there something wrong in the question unless I am not understanding it correctly?

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Re: At a certain laboratory, chemical substance are identified by an unord [#permalink]

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New post 15 Jan 2016, 20:22
rachitshah wrote:
Bunuel wrote:
amidamani13 wrote:
At a certain laboratory, chemical substance are identified by an unordered combination of three different colors. If no chemical may be assigned the same three colors as any other, what is the maximum number of substances that can be identified using seven colors?

A) 21
B) 35
C) 105
D) 135
E) 210

Looking for easier method to solve this.


Check Constructing Numbers, Codes and Passwords in our Special Questions Directory.


Hello Bunuel,

Since the question says it is unordered and no chemical can have same 3 colors -> This should not omit the possibility of 2 same colors in 3 color combination right?
I was looking for an option which has 7*7*5 maximum number of substances.
Isn't there something wrong in the question unless I am not understanding it correctly?


Hi rachit,
7*7*5 as per you also includes combination of two same colour and one different colour also.
But look at the coloured portion, it clearly specifies three different colour...
your solution would be close to correct if it said that all three colours can not be the same
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Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

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Re: At a certain laboratory, chemical substances [#permalink]

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New post 06 Sep 2016, 16:26
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sidoknowia wrote:
At a certain laboratory, chemical substances are identifies by an unordered combination of 3 colors. If no chemical may be assigned the same 3 colors, what is the maximum number of substances that can be identified using 7 colors?

21
35
105
135
210



3 out of 7 can be chosen in 7C3 ways
chosen 3 colors can be arranged in 3! ways

so answer should be 7c3 * 3!

Am I correct? if not, what am I doing wrong?
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Re: At a certain laboratory, chemical substances [#permalink]

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New post 06 Sep 2016, 19:00
Hi sidoknowia,

The prompt tells us that substance is identified by an UNORDERED combination of 3 colors and that no chemical may be assigned the same 3 colors as any other chemical.

As an example, a chemical with the colors A/B/C means that the following combinations CANNOT be used by any other chemical:

ABC
ACB
BAC
BCA
CAB
CBA

By extension, the first part of your calculation would be the number of possible substances that could be identified with 7 colors: 7c3 = 35 possible substances

Final Answer:
[Reveal] Spoiler:
B


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Re: At a certain laboratory, chemical substance are identified by an unord [#permalink]

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Re: At a certain laboratory, chemical substance are identified by an unord   [#permalink] 26 Oct 2017, 10:14
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