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A certain stock exchange designates each stock with a 1, 2 [#permalink]

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26 Oct 2009, 13:25

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32% (02:06) wrong based on 400 sessions

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A certain stock exchange designates each stock with a 1, 2 or 3 letter code, where each letter is selected from the 26 letters of the alphabet. If the letters may be repeated and if the same letters used in a different order, constitute a different code, how many diff stocks is it possible to designate with these codes?

I think that I should be using permutations as order does matter here, but I am still not getting the answer: P of 26 taken by 3 = 15,600 P of 26 taken by 2 = 650 P of 26 taken by 1 = 26 adding them does not give me the right answer still.

Can smb please help me to understand the below problem?

A certain stock exchange designates each stock with a 1, 2 or 3 letter code, where each letter is selected from the 26 letters of the alphabet. If the letters may be repeated and if the same letters used in a different order, constitute a different code, how many diff stocks is it possible to designate with these codes? A: 2,951 B: 8,125 C:15,600 D: 16,302 E: 18,278

They say that QA is E, however I am not sure how to get there.

I have C 26 taken by 3 = 2,600 C of 26 taken by 2 = 325 C of 26 taken by 1 = 26. If I add these, I get answer A. Not sure what I am doing wrong.

Thank you, Andreea

1 letter code - 26 (or you can write 26C1) 2 letter code - 26*26=26^2 (or you can write 26C1*26C1=26^2) 3 letter code - 26*26*26=26^3 (or you can write 26C1*26C1*26C1=26^3)

(For 2 letter, for example, you have 26 choices per each letter, it's 26^2 and not 26C2 or 26P2.)

Re: A certain stock exchange designates each stock with a 1, 2 [#permalink]

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02 Dec 2013, 01:01

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Can smb please help me to understand the below problem?

A certain stock exchange designates each stock with a 1, 2 or 3 letter code, where each letter is selected from the 26 letters of the alphabet. If the letters may be repeated and if the same letters used in a different order, constitute a different code, how many diff stocks is it possible to designate with these codes? A: 2,951 B: 8,125 C:15,600 D: 16,302 E: 18,278

They say that QA is E, however I am not sure how to get there.

I have C 26 taken by 3 = 2,600 C of 26 taken by 2 = 325 C of 26 taken by 1 = 26. If I add these, I get answer A. Not sure what I am doing wrong.

Thank you, Andreea

1 letter code - 26 (or you can write 26C1) 2 letter code - 26*26=26^2 (or you can write 26C1*26C1=26^2) 3 letter code - 26*26*26=26^3 (or you can write 26C1*26C1*26C1=26^3)

(For 2 letter, for example, you have 26 choices per each letter, it's 26^2 and not 26C2 or 26P2.)

Re: A certain stock exchange designates each stock with a 1, 2 [#permalink]

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08 Dec 2014, 11:40

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
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A certain stock exchange designates each stock with a 1, 2 [#permalink]

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23 Dec 2015, 10:58

Bunuel wrote:

ralucaroman wrote:

HI,

Can smb please help me to understand the below problem?

A certain stock exchange designates each stock with a 1, 2 or 3 letter code, where each letter is selected from the 26 letters of the alphabet. If the letters may be repeated and if the same letters used in a different order, constitute a different code, how many diff stocks is it possible to designate with these codes? A: 2,951 B: 8,125 C:15,600 D: 16,302 E: 18,278

They say that QA is E, however I am not sure how to get there.

I have C 26 taken by 3 = 2,600 C of 26 taken by 2 = 325 C of 26 taken by 1 = 26. If I add these, I get answer A. Not sure what I am doing wrong.

Thank you, Andreea

1 letter code - 26 (or you can write 26C1) 2 letter code - 26*26=26^2 (or you can write 26C1*26C1=26^2) 3 letter code - 26*26*26=26^3 (or you can write 26C1*26C1*26C1=26^3)

(For 2 letter, for example, you have 26 choices per each letter, it's 26^2 and not 26C2 or 26P2.)

Total =26+26^2+26^3 =18,278

Possibly foolish question, but why are we adding instead of multiplying the 26's? I've been doing all these combinatorics questions and it's almost always multiplying possibilities not adding them. Just curious what the difference is that changes why we'd add versus multiply in these kinds of situations.
_________________

Re: A certain stock exchange designates each stock with a 1, 2 [#permalink]

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23 Dec 2015, 12:41

what about the case of AA, BB, CC...Wouldn't we have to consider these as 1 instead of double counting them.

I had them as 26+(26*26/2)+(26*26*26)/6. What am I doing wrong?

Bunuel wrote:

ralucaroman wrote:

HI,

Can smb please help me to understand the below problem?

A certain stock exchange designates each stock with a 1, 2 or 3 letter code, where each letter is selected from the 26 letters of the alphabet. If the letters may be repeated and if the same letters used in a different order, constitute a different code, how many diff stocks is it possible to designate with these codes? A: 2,951 B: 8,125 C:15,600 D: 16,302 E: 18,278

They say that QA is E, however I am not sure how to get there.

I have C 26 taken by 3 = 2,600 C of 26 taken by 2 = 325 C of 26 taken by 1 = 26. If I add these, I get answer A. Not sure what I am doing wrong.

Thank you, Andreea

1 letter code - 26 (or you can write 26C1) 2 letter code - 26*26=26^2 (or you can write 26C1*26C1=26^2) 3 letter code - 26*26*26=26^3 (or you can write 26C1*26C1*26C1=26^3)

(For 2 letter, for example, you have 26 choices per each letter, it's 26^2 and not 26C2 or 26P2.)

Total =26+26^2+26^3 =18,278

gmatclubot

Re: A certain stock exchange designates each stock with a 1, 2
[#permalink]
23 Dec 2015, 12:41

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