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A certain stock exchange designates each stock with a 1, 2

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

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New post 26 Oct 2009, 13:25
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A
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68% (02:25) correct 32% (01:58) wrong based on 346 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?

A: 2,951
B: 8,125
C: 15,600
D: 16,302
E: 18,278

[Reveal] Spoiler:
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
[Reveal] Spoiler: OA
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Re: Combinations - Powerprep [#permalink]

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New post 26 Oct 2009, 13:40
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.
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Re: Combinations - Powerprep [#permalink]

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New post 26 Oct 2009, 13:57
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Pretty simple actually
Number of 1 letter symbols = 26
Number of 2 letter symbols = 26*26
Number of 3 letter symbols = 26*26*26

The answer is sum of the 3. However if you are a real GMAT club member and confident about your approach you won't calculate any further.

The answer choices have their units digits unique. All 3 of the above end in 6 (6 to the power of anything ends in 6) so 6+6+6 = 18 i.e. ends with 8.

So the answer is E.
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Last edited by atish on 26 Oct 2009, 14:13, edited 1 time in total.
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Re: Combinations - Powerprep [#permalink]

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New post 26 Oct 2009, 14:08
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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
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Re: Combinations - Powerprep [#permalink]

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New post 26 Oct 2009, 14:20
Thank you, guys. I understand now. Appreciate your help.
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Re: A certain stock exchange designates each stock with a 1, 2 [#permalink]

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New post 02 Dec 2013, 01:01
Hello from the GMAT Club BumpBot!

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Re: Combinations - Powerprep [#permalink]

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New post 02 Dec 2013, 01:47
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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


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Hope this helps.
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PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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

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New post 08 Dec 2014, 11:40
Hello from the GMAT Club BumpBot!

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

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New post 30 Nov 2015, 07:35
Hi I have a doubt:

by doing 26^3 are you not counting palindromes? I mean, for example ABA would not be double counted?
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Re: A certain stock exchange designates each stock with a 1, 2 [#permalink]

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New post 30 Nov 2015, 15:10
lolivaresfer wrote:
Hi I have a doubt:

by doing 26^3 are you not counting palindromes? I mean, for example ABA would not be double counted?


It's fine since the question mentions: "the same letters used in a different order, constitute a different code"
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A certain stock exchange designates each stock with a 1, 2 [#permalink]

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

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