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

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VP
Joined: 22 Nov 2007
Posts: 1079

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

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19 Dec 2007, 06:09
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

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 repeatyed and if the same letters used in a different order constitute a different code, how many different stocks is it possibile to uniquely designate with these codes?

A.2951
B.8125
C.15600
D. 16302
E.18278

Kudos [?]: 678 [0], given: 0

CEO
Joined: 17 Nov 2007
Posts: 3584

Kudos [?]: 4584 [0], given: 360

Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40

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19 Dec 2007, 07:32
E

N=26+26^2+26^3=18278.

The shortcut for calculation:

last digit of 26: 6
last digit of 26^2: 6
last digit of 26^3: 6
last digit of the sum: 8

Therefore, E

Kudos [?]: 4584 [0], given: 360

Senior Manager
Joined: 06 Mar 2006
Posts: 490

Kudos [?]: 269 [0], given: 1

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19 Dec 2007, 07:33
26+26*26+26*26*26=18278

Kudos [?]: 269 [0], given: 1

VP
Joined: 22 Nov 2007
Posts: 1079

Kudos [?]: 678 [0], given: 0

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19 Dec 2007, 08:05
I thought: 1c26+2c26+3c26...where's my mistake?

Kudos [?]: 678 [0], given: 0

CEO
Joined: 17 Nov 2007
Posts: 3584

Kudos [?]: 4584 [0], given: 360

Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40

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19 Dec 2007, 08:10
marcodonzelli wrote:
I thought: 1c26+2c26+3c26...where's my mistake?

1. " the letters may be repeatyed" leads to 26*26*26..... instead of 26*25*24 for nPm-nCm approach

2. "the same letters used in a different order constitute a different code" would lead rather nPm than nCm.

Kudos [?]: 4584 [0], given: 360

CEO
Joined: 29 Mar 2007
Posts: 2554

Kudos [?]: 516 [0], given: 0

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19 Dec 2007, 14:20
marcodonzelli wrote:
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 repeatyed and if the same letters used in a different order constitute a different code, how many different stocks is it possibile to uniquely designate with these codes?

A.2951
B.8125
C.15600
D. 16302
E.18278

This wasn't too difficult, just may seem so b/c we don't usually encounter these types of perm problems..

26 for 1 letter codes

26*26 for 2 letter codes

26*26*26 for three letter codes

26+676+17576=18278

E

Kudos [?]: 516 [0], given: 0

Director
Joined: 03 Sep 2006
Posts: 865

Kudos [?]: 1070 [0], given: 33

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21 Dec 2007, 22:19
marcodonzelli wrote:
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 repeatyed and if the same letters used in a different order constitute a different code, how many different stocks is it possibile to uniquely designate with these codes?

A.2951
B.8125
C.15600
D. 16302
E.18278

If repetition is allowed:

26 + 26*26 + 26*26*26

I am not sure how to calculate it faster.

Kudos [?]: 1070 [0], given: 33

Director
Joined: 03 Sep 2006
Posts: 865

Kudos [?]: 1070 [0], given: 33

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21 Dec 2007, 22:21
walker wrote:
E

N=26+26^2+26^3=18278.

The shortcut for calculation:

last digit of 26: 6
last digit of 26^2: 6
last digit of 26^3: 6
last digit of the sum: 8

Therefore, E

This short cut for calculation is awesome! Thanks Walker!

Kudos [?]: 1070 [0], given: 33

SVP
Joined: 04 May 2006
Posts: 1881

Kudos [?]: 1399 [0], given: 1

Schools: CBS, Kellogg

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22 Dec 2007, 01:56
LM wrote:
walker wrote:
E

N=26+26^2+26^3=18278.

The shortcut for calculation:

last digit of 26: 6
last digit of 26^2: 6
last digit of 26^3: 6
last digit of the sum: 8

Therefore, E

This short cut for calculation is awesome! Thanks Walker!

Walker,
There is a gap in my knowledge of this problem. I can understand only the case 26*26*26. B/c the codes can be designate by 26C1*26C1*26C1. Can Walker make clear why I must plus 26 and 26*26?

Many thanks

Kudos [?]: 1399 [0], given: 1

CEO
Joined: 17 Nov 2007
Posts: 3584

Kudos [?]: 4584 [0], given: 360

Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40

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22 Dec 2007, 02:39
sondenso wrote:
Walker make clear why I must plus 26 and 26*26?

"A certain stock exchange designates each stock with a 1,2 or 3-letter code"

You should calculate separately for 1-letter code, 2-letter code and 3-letter code and sum them.

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Intern
Joined: 22 Dec 2007
Posts: 1

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22 Dec 2007, 02:53
The solution will be 26+26*26+26*26*26
The shortcut can look like this 26+26*26+26*26*26=26*(1+26+26*26)=
=26*(1+26*(1+26))=26*(1+26*27)=18278

The advantage is that it is not a guess-like strategy, but a more reliable one.

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22 Dec 2007, 02:53
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