Exercise 10 Page 841

Many country codes are $3\text{-}$digit numbers. We want to find the number of all possible different $3\text{-}$digit country codes. To do so, we need to first evaluate how many different choices there are for each digit. Let's list the numbers we can choose from. There are $10$ single-digit numbers to pick from. We know there are no restrictions regarding second and third digits of the code, so they can be chosen from all $10$ numbers. However, there is a restriction on the first digit. Country codes do not begin with a $0$ or $1.$ Therefore, the first digit can be chosen from only $8$ numbers.

Number of Choices
First Digit	Second Digit	Third Digit
$8$	$10$	$10$

In order to find the number of all possible codes, we need to use the Fundamental Counting Principle.

Fundamental Counting Principle

If an event $M$ occurs in $m$ ways and event $N$ occurs in $n$ ways, then event $M$ followed by event $N$ can occur in $m\cdot n$ ways.

The Fundamental Counting Principle also works for more than two events. We need to multiply the number of possible choices for all three digits.

Let's substitute the numbers of choices and evaluate the total number of possible different $3\text{-}$digit country codes.