A company assigns product codes consisting of all the letters in the alphabet.How many product codes are possible if the company uses at most 3 letters in its codes, and all letters can be repeated in any one code? Choose one.
A) 15600 B) 16226 C) 17576 D) 18278 E) 28572
1-letter codes   26 letters, so there are 26 possible codes   2-letter codes   There are 26 options for the 1st letter, and 26 options for the 2nd letter.   So, the number of 2-letter codes = (26)(26) = 26²   3-letter codes   There are 26 options for the 1st letter, 26 options for the 2nd letter, and 26 options for the 3rd letter.   So, the number of 3-letter codes = (26)(26)(26) = 26³   So, the TOTAL number of codes = 26 + 26² + 26³=18278   ANSWER:18278
<result>D</result>
A company assigns product codes consisting of all the letters in the alphabet.How many product codes are possible if the company uses at most 3 letters in its codes, and all letters can be repeated in any one code?