Exercise 1.2

Question

\begin{enumerate}[label=(\alph*)]
\item How many 7-digit phone numbers are possible, assuming that the first digit can’t be a 0 or a 1?
\item Re-solve (a), except now assume also that the phone number is not allowed to start
with 911 (since this is reserved for emergency use, and it would not be desirable for the
system to wait to see whether more digits were going to be dialed after someone has
dialed 911).
\end{enumerate}

fifthist x · Accepted Answer

\begin{enumerate}[label=(\alph*)]
\item If the first digit can't be $0$ or $1$, we have eight choices for the 
first digit. The remaining six digits can be anything from $0$ to $9$. Hence, 
the solution is
  $$ 8 	imes 10^{6}$$

\item We can subtract the number of phone numbers that start with $911$ from 
the total number of phone numbers we found in the previous part.

If a phone number starts with $911$, it has ten choices for each of the 
remaining four digits.

$$ 8 	imes 10^{6} - 10^{4} $$
\end{enumerate}

Exercise 1.2

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Exercise 1.2

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