Local phone numbers consist of seven numerals, the first three of which are common to many users. A small town's phone numbers all start with 336,

Question

Local phone numbers consist of seven numerals, the first three of which are common to many users. A small town's phone numbers all start with 336,

354,
or 364.
How many phone numbers are available? (The area code is not included.)

(Give an exact answer. Use symbolic notation and fractions where needed.)

Answer 1

There are 7 digits in a local phone number, with the first 3 being set to either 336, 354, or 364. This leaves 4 digits that can be any numeral between 0 and 9.

For each of the 4 remaining digits, there are 10 possible numerals (0-9), so there are a total of 10 * 10 * 10 * 10 = 10^4 = 10,000 possible combinations for those 4 digits.

Since there are 3 possible sets of starting digits (336, 354, or 364), there are a total of 3 * 10,000 = 30,000 phone numbers available in the small town.