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PS combinatorics

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lionheart
 Post subject: PS combinatorics
 Post Posted: Thu May 29, 2008 9:30 am 
A certain stock exchange designates each stock with a one-, two-, or three- 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

Answer is E, please explain
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m&m
 Post subject:
 Post Posted: Sat May 31, 2008 2:28 am 
Hope the following explanation will help.

There are one, two, or three letter code:

one letter code: 26 choices
two letter code: 26 X 26 (as the letters may be repeated)
three letter code: 26 x 26 x 26

(26) + (26 x 26) + (26 x 26 x 26) = 18278
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RonPurewal
 Post subject:
 Post Posted: Thu Jun 05, 2008 5:38 am 
Offline
ManhattanGMAT Staff


Posts: 7146
m&m wrote:
Hope the following explanation will help.

There are one, two, or three letter code:

one letter code: 26 choices
two letter code: 26 X 26 (as the letters may be repeated)
three letter code: 26 x 26 x 26

(26) + (26 x 26) + (26 x 26 x 26) = 18278


correct.

by the way, note that there is no need to actually calculate this value. if you just examine the units digits of the numbers you're to multiply together - 6, 6, 6 - you'll realize that the result must end with an '8'. there is only one such answer choice.
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