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

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VP
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A certain stock exchange designates each stock with a 1 , 2 [#permalink]  21 Jan 2008, 10:01
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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 different stocks is it possible to uniquely designate with these codes?

A.2951
B.8125
C.15600
D.16302
E.18278
CEO
Joined: 29 Mar 2007
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Re: repetition [#permalink]  21 Jan 2008, 18:07
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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 repeated and if the same letters used in a different order constitute a different code , how many different stocks is it possible to uniquely designate with these codes?

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

26 for the first letter 26^2 for the second 26^3 for the third.

26+26^2+26^3.

To elim the need for calculations just realize that the units digit will be 6 and there are three 6's.

So the units digit will be 8.

E
Director
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Re: repetition [#permalink]  21 Jan 2008, 10:23
26^1+26^2+26^3 = 18,278 (E)
VP
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Re: repetition [#permalink]  18 Mar 2008, 08:03
GMATBLACKBELT wrote:
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 repeated and if the same letters used in a different order constitute a different code , how many different stocks is it possible to uniquely designate with these codes?

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

26 for the first letter 26^2 for the second 26^3 for the third.

26+26^2+26^3.

To elim the need for calculations just realize that the units digit will be 6 and there are three 6's.

So the units digit will be 8.

E

so we have permutations with repetitions. given 26 elements we want to select them no more than 3 times (1,2,3 letter codes), with repetitions allowed. thus we have 26+26^2+26^3, simply as it is
Re: repetition   [#permalink] 18 Mar 2008, 08:03
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# A certain stock exchange designates each stock with a 1 , 2

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