Question

3. In a particular area code, how many phone numbers (###-####) are possible? The first digit cannot be a zero, and assume digits can be repeated.

Answer 1

10 billion phone numbers.

Explanation:

Answer 2

Answer: 9 million possibilities

Explanation:

Considering that each digit is selected independently of the others, it is a consequence of the statement that says digits can be repeated.

The first digit chosen can be any of 1 through 9. And it can be selected in nine different ways. Then the remaining digit can then be selected in 10 ways, as zero can be used.

Since each choice of digit is independent, you can multiply all these choices together:

N = 9 × 10 × 10 × 10 × 10 × 10 × 10 =

9 million possibilities.

This is the reason why area codes are used.