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 [tex]8*10*10*10*10*10*10=8* 10^{6} [/tex] possible numbers.
b.
consider the numbers which start with 911. There are [tex]10*10*10*10=10 ^{4} [/tex] 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 [tex]8* 10^{6}-10^{4}=7,990,000[/tex] numbers which don't start with 911.
Answer:
a.[tex]8*10^{6}[/tex]
b.7,990,000
