Chapter 4.8, Problem 247E

Zip Codes. The author spoke with a representative of the U.S. Postal Service and obtained the following information about zip codes. A five-digit zip code consists of five digits, of which the first three give the sectional center and the last two the post office or delivery area. In addition to the five-digit zip code, there is a trailing plus four zip code. The first two digits of the plus four zip code give the sector or several blocks and the last two the segment or side of the street. For the five-digit zip code, the first four digits can be any of the digits 0–9 and the fifth any of the digits 1–8. For the plus four zip code, the first three digits can be any of the digits 0–9 and the fourth any of the digits 1–9.

1. a. How many possible five-digit zip codes are there?
2. b. How many possible plus four zip codes are there?
3. c. How many possibilities are there in all, including both the five-digit zip code and the plus four zip code?