1. (Possible Outcomes) A telephone number in North America consists of a three-digit area code, followed by a three-digit exchange, followed by a four-digit extension. The area code cannot start with a 0 or 1, nor can the exchange. Other than that, any digit 0-9 can be used.
a. How many different seven-digit phone numbers (ignoring the area code) can be formed? Can a city of 2 million people be served by a single area code? Explain.
b. How many exchanges are needed to serve a city of 80,000 people? (Hint: How many extensions in one exchange?)
c. How many area codes are possible?
d. How many 10-digit phone numbers are possible?
e. How many people are there in the U.S.? Do you believe the statement that we are running out of phone numbers? Explain.
f. Let's assume we are running out of area codes (and thus phone numbers). What can they do to reduce the shortage of phone numbers?
g. Not too long ago, an area code had to have a 0 or 1 in the middle digit (do you remember those days?). With this additional rule, how many area codes were possible?