ak2121 wrote:
Bunuel wrote:
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
1 letter codes = 26
2 letter codes = 26^2
3 letter codes = 26^3
Total = 26 + 26^2 + 26^3
The problem we are faced now is how to get the answer quickly. Note that the units digit of 26+26^2+26^3 would be (6+6+6=18) 8. Only one answer choice has 8 as unit digit: E (18,278). So I believe, even not calculating 26+26^2+26^3, that answer is E.
Hi, should'nt we subtract 26 from 26^2 and 26^3 because AA,BB, CC or BBB,CCC,DDD will be occuring twice in the case?
26^2 gives the number of
two-letter codes (this number includes same-letter codes: AA, BB, ...)
26^3 gives the number of
three-letter codes (this number includes same-letter codes: AAA, BBB, ...)
As you can see there is not overlap between codes given by 26^2 and 26^3.