Answer to Question #155625 in Combinatorics | Number Theory for leosayas04

Question

In a certain country telephone numbers have 9 digits. The first two digits are the area

code (03) and are the same within a given area. The last 7 digits are the local number and

cannot begin with 0. How many different telephone numbers are possible within a given

area code in this country?

Answer 1

A possible number has the following structure:(03)xxxxxxx. The number can not begin with 0. It means that we can choose 9 diferent numbers for the first position and 10 different numbers for other positions. Using multiplication rule from combinatorics, we receive: $9\cdot10^6=9000000$ different phone numbers.