1. an area code had to have a 0 or 1 in the middle digit. How many 10-digit phone numbers were possible?

Question

1. an area code had to have a 0 or 1 in the middle digit. How many 10-digit phone numbers were possible?

Answer 1

Hi Arielle, 

 

you have 10-digit phone numbers. 

 

The first digit can not be 0 so it has 9 possibilities (from  1 to 9)

The second digit can only be 0 or 1 so it has only 2 possibilities

The remaining 8 digits has 10 possibilities each (0 to 9)

 

so you have 9 x 2 x 10⁸ = 1,800,000,000 possible numbers

 

 

Answer 2

Under the conditions that you provide (which no longer apply*), and with another limitation, that the leading digit of the area code cannot be 0 or 1 and this restriction also applies to the first position of the 7-digit phone number...

 

first digit of area code: 8 choices (2 thru 9)

second digit: 8 choices (excluding 0 or 1)

third digit of area code: ten choices

 

Next seven digits are the phone number; first one cannot be 0 or 1, either--8 choices

Each of the remaining six digits of the phone number: ten choices each (repetition allowed).

 

Multiplying all these together: 8•8•10•8•10•10•10•10•10•10 = 10⁷•8³ = 5 120 000 000

 

*  in L.A. there's an area code 323