Answer
a) There are 8 possibilities for the first digit and 10 possibilities for each digit afterwards
b) $8000000$
Work Step by Step
a)
The first digit of the phone number cannot contain the digits $0$ and $1$, so it can contain the digits from $2$ to $9$ inclusive, which allows for $8$ possible digits. The second through seventh digit have no restrictions, so it can contain the digits from $0$ to $9$ inclusive, which allows for $10$ possible digits
b) For the first digit, there are $8$ possible digits allowed (refer to part a) and for the second through seventh there are $10$ possible digits allowed (refer to part a).
$\square{}$ $\square{}$ $\square{}$ $\square{}$ $\square{}$ $\square{}$ $\square{}$
Fill up each box with the number of possibilities you can have for each digit. Multiply all the numbers in the boxes together to get the number of possibilites there are.
$8 \times 10\times10\times10\times10\times10\times10$
$8 \times 10^6$
$8000000$
There are $8000000$ possible phone numbers.
