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# A certain stock exchange designates each stock with one, two

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Senior Manager
Joined: 08 Aug 2005
Posts: 251
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A certain stock exchange designates each stock with one, two [#permalink]  26 Apr 2006, 01:33
A certain stock exchange designates each stock with one, two or three letter code, where each letter is selected from 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?

2951
8125
15600
16302
18278
VP
Joined: 29 Apr 2003
Posts: 1405
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Kudos [?]: 18 [0], given: 0

for 3 letters

we have 26x26x26 combinations!

for 2, we have 26x26
for 1, we have 26

Adding all of them = 18278.
Hence, E
Manager
Joined: 23 Mar 2006
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Hey,

a similar one you may hit upon, when the codes can be 4 letters OR 5 letters - answer is (26)^4*27.
GMAT Club Legend
Joined: 07 Jul 2004
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Location: Singapore
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The number of ways to pick a 3 letter code = 26^3
The number of ways to pick a 2 letter code = 26^2
The number of ways to pick a 1 letter code = 26

Total = 26^3 + 26^2 + 26 = 26(26^2 + 26 + 1) = 18278
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