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 letter 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) 15302
E) 18278
Answer: E
Total ways to pick a 3 letter code = 26*26*26 = 26^3
Total ways to pick a 2 letter code = 26*26 = 26^2
Total ways to pick a 1 letter code = 26
Thus total stocks: 26^3 + 26^2 + 26 = 26(26^2 + 26 + 1) = 18278
