Chapter 6 - Section 6.3 - Decision Algorithms: The Addition and Multiplication Principles - Exercises - Page 425: 36

$182,780$

There are 10 possible digits. There are 26 letters in the alphabet. So if the ID code is one letter, followed by a digit, there are $26*10=260$ possibilities.. If the ID code is two letters, followed by a digit, there are $26*26*10=6,760$ possibilities.. If the ID code is three letters, followed by a digit, there are $26*26*26*10=175,760$ possibilities.. Overall, there are $260+6,760+175,760=182,780$ different employee codes.