Question

a telephone company wants to create as many 7-digit phone numbers as possible without changing the first 3 digits. How many phone numbers can be created?

Answer 1

To figure this one out, you have to first see how many possible numbers could go in the last four digits. Think of it this way, since they want the first three digits to be the same, the phone numbers could be 555-____, where in each underscore you can have any number from 0-9. Through this reasoning, you get 10 possible choices for each dash. Your next step would be to take the 10 choices, and give it a power of four (since three of the digits are chosen), making your answer 10^4=10000 possible numbers.