How many 7-digit phone numbers are possible, assuming that the first digit can’t be a 0 or a 1? (b) re-solve (a), except now assume also that the phone number is not allowed to start with 911?

A. We are going to form 7 digit numbers from the set {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}

where the first digit cannot be 0 or 1.

so we have 8 choices for the 1. digit, and 10 choices for all the other 6 digits.

this means there are  possible numbers.

b.

consider the numbers which start with 911. There are  such numbers, since for the 4th, 5th, 6th and 7th digits we have 10 choices.

then we remove this number, from the one we found in a:

There are in total  numbers which don't start with 911.

a.
b.7,990,000

Provide an equation