Question

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?

Answer 1

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 $8*10*10*10*10*10*10=8* 10^{6}$ possible numbers.

b.

consider the numbers which start with 911. There are $10*10*10*10=10 ^{4}$ 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 $8* 10^{6}-10^{4}=7,990,000$ numbers which don't start with 911.


Answer:

a.$8*10^{6}$
b.7,990,000