Chapter 6 - Section 6.3 - Decision Algorithms: The Addition and Multiplication Principles - Exercises - Page 425: 39b

$30,000$

There are 10 different digits, If the number starts with 463, the other 4 digits can be 10 different digits. This gives $10^4=10,000$ telephone numbers. If the number starts with 460, the other 4 digits can be 10 different digits. This gives $10^4=10,000$ telephone numbers. If the number starts with 400, the other 4 digits can be 10 different digits. This gives $10^4=10,000$ telephone numbers. Therefore there are $10,000+10,000+10,000=30,000$ telephone numbers that start with either 463, 460, or 400