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Code in alphabetical order

This topic has 3 expert replies and 1 member reply
imawolf Newbie | Next Rank: 10 Posts Default Avatar
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Posted:
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Code in alphabetical order

Post Wed Sep 13, 2017 7:38 am
A store labels its products with three digits codes composed entirely of letters of the alphabet arranged alphabetically. How many such codes can be created?

(A) 2600
(B) 2936
(C) 9630
(D) 14526
(E) 17576

Totally puzzled. How to solve this?

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Matt@VeritasPrep GMAT Instructor
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Post Wed Sep 20, 2017 4:09 pm
Let me add a step here, since calculating 26 choose 3 isn't the most natural thing in the world:

26 choose 3 =

26! / (23! * 3!) =

(26 * 25 * 24) / (3 * 2 * 1) =

26/2 * 24/3 * 25/1 =

13 * 8 * 25 =

13 * 200 =

2600

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imawolf Newbie | Next Rank: 10 Posts Default Avatar
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Post Wed Sep 13, 2017 6:24 pm
Very clear! Thanks Brent!

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Post Wed Sep 13, 2017 7:50 am
imawolf wrote:
A store labels its products with three digits codes composed entirely of letters of the alphabet arranged alphabetically. How many such codes can be created?

(A) 2600
(B) 2936
(C) 9630
(D) 14526
(E) 17576
Take the task of creating a 3-letter code and break it into stages.

Stage 1: Select 3 letters from the alphabet
Since the order in which we select the letters does not matter, we can use combinations.
We can select 3 letters from 26 letters in 26C3 ways (2600 ways)
So, we can complete stage 1 in 2600 ways

Stage 2: Arrange the 3 letters in alphabetical order
IMPORTANT: Once we have selected 3 letters in stage 1, this next step can be accomplished in only 1 way.
For example, if we selected G, B and R in stage 1, then there's only one way to arrange these letters alphabetically (BGR)
So we can complete stage 2 in 1 way

By the Fundamental Counting Principle (FCP), we can complete the 2 stages (and thus create a 3-letter code) in (2600)(1) ways (= 2600 ways)

Answer: A
--------------------------

Note: the FCP can be used to solve the MAJORITY of counting questions on the GMAT. For more information about the FCP, watch our free video: http://www.gmatprepnow.com/module/gmat-counting/video/775

You can also watch a demonstration of the FCP in action: https://www.gmatprepnow.com/module/gmat-counting/video/776

Then you can try solving the following questions:

EASY
- http://www.beatthegmat.com/what-should-be-the-answer-t267256.html
- http://www.beatthegmat.com/counting-problem-company-recruitment-t244302.html
- http://www.beatthegmat.com/picking-a-5-digit-code-with-an-odd-middle-digit-t273110.html
- http://www.beatthegmat.com/permutation-combination-simple-one-t257412.html
- http://www.beatthegmat.com/simple-one-t270061.html


MEDIUM
- http://www.beatthegmat.com/combinatorics-solution-explanation-t273194.html
- http://www.beatthegmat.com/arabian-horses-good-one-t150703.html
- http://www.beatthegmat.com/sub-sets-probability-t273337.html
- http://www.beatthegmat.com/combinatorics-problem-t273180.html
- http://www.beatthegmat.com/digits-numbers-t270127.html
- http://www.beatthegmat.com/doubt-on-separator-method-t271047.html
- http://www.beatthegmat.com/combinatorics-problem-t267079.html


DIFFICULT
- http://www.beatthegmat.com/wonderful-p-c-ques-t271001.html
- http://www.beatthegmat.com/permutation-and-combination-t273915.html
- http://www.beatthegmat.com/permutation-t122873.html
- http://www.beatthegmat.com/no-two-ladies-sit-together-t275661.html
- http://www.beatthegmat.com/combinations-t123249.html


Cheers,
Brent

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Brent Hanneson – Founder of GMATPrepNow.com
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Post Wed Sep 13, 2017 6:13 pm
Hi imawolf,

What is the source of this question? I ask because it does not include many of the 'details' that an Official question would likely include. For example, it refers to 'three digit' codes when it's clearly meant to infer 'three-letter' codes. We're meant to infer that we're dealing with the 26-letter English alphabet, but the prompt never explicitly states that and we're also meant to infer that duplicate letters are NOT allowed (which the prompt also does not state).

Assuming all of those details though, then Brent's solution is spot-on. That having been said, if this lack of attention-to-detail is typical in the questions that came from this source, then you might want to work with a different resource that provides more reputable study materials.

GMAT assassins aren't born, they're made,
Rich

_________________
Contact Rich at Rich.C@empowergmat.com

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