Question

Suppose that at some future time every telephone in the
world is assigned a number that contains a country code
1 to 3 digits long, that is, of the form X, XX, or XXX,
followed by a 10-digit telephone number of the form
NXX-NXX-XXXX (as described in Example 8). How
many different telephone numbers would be available
worldwide under this numbering plan?

Answer 1

Using the Fundamental Counting Theorem, it is found that $1.11 \times 10^{13}$ different telephone numbers would be avaiable worldwide.

What is the Fundamental Counting Theorem?

It is a theorem that states that if there are n things, each with $n_1, n_2, \cdots, n_n$ ways to be done, each thing independent of the other, the number of ways they can be done is:

$N = n_1 \times n_2 \times \cdots \times n_n$

In this problem:

• For the code, considering that for each digit there are 10 possible outcomes, the number of options is $n_1 = 10 + 10^2 + 10^3 = 1110 = 1.11 \times 10^3$.

• For the number, there are 10 digits, each with 10 options, hence the number of options is $n_2 = 10^{10}$.

Hence, the number of different telephone numbers that would be avaiable is given by:

$N = n_1n_2 = 1.11 \times 10^3 \times 10^{10} = 1.11 \times 10^{13}$

$1.11 \times 10^{13}$ different telephone numbers would be avaiable worldwide.

More can be learned about the Fundamental Counting Theorem at https://brainly.com/question/24314866