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

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VP
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A certain stock exchange designates each stock with a 1,2 or [#permalink]  19 Dec 2007, 05:09
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
CEO
Joined: 17 Nov 2007
Posts: 3578
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Followers: 406

Kudos [?]: 2133 [0], given: 359

Expert's post
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
Senior Manager
Joined: 06 Mar 2006
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Kudos [?]: 91 [0], given: 1

26+26*26+26*26*26=18278

VP
Joined: 22 Nov 2007
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I thought: 1c26+2c26+3c26...where's my mistake?
CEO
Joined: 17 Nov 2007
Posts: 3578
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
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Kudos [?]: 2133 [0], given: 359

Expert's post
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.
CEO
Joined: 29 Mar 2007
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Re: permutations - DIFFICULT [#permalink]  19 Dec 2007, 13:20
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
Director
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Re: permutations - DIFFICULT [#permalink]  21 Dec 2007, 21:19
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.
Director
Joined: 03 Sep 2006
Posts: 885
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Kudos [?]: 256 [0], given: 33

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!
SVP
Joined: 04 May 2006
Posts: 1936
Schools: CBS, Kellogg
Followers: 19

Kudos [?]: 434 [0], given: 1

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
CEO
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Posts: 3578
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Kudos [?]: 2133 [0], given: 359

Expert's post
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.
Intern
Joined: 22 Dec 2007
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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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