Can smb please help me to understand the below problem?
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 diff stocks is it possible to designate with these codes?
They say that QA is E, however I am not sure how to get there.
I have C 26 taken by 3 = 2,600
C of 26 taken by 2 = 325
C of 26 taken by 1 = 26.
If I add these, I get answer A. Not sure what I am doing wrong.
1 letter code - 26 (or you can write 26C1)
2 letter code - 26*26=26^2 (or you can write 26C1*26C1=26^2)
3 letter code - 26*26*26=26^3 (or you can write 26C1*26C1*26C1=26^3)
(For 2 letter, for example, you have 26 choices per each letter, it's 26^2 and not 26C2 or 26P2.)
Total =26+26^2+26^3 =18,278