PS combinatorics

by **lionheart** 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

by **m&m** 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

by **RonPurewal** Thu Jun 05, 2008 5:38 am

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.