Question

You have been assigned a 9 digit identification number.

Explain why you should use a Fundamental Counting Principle?

How many identification numbers are possible?
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Answer 1

1,000,000,000 identification numbers are possible.

Explanation:

We are assigned a 9 digit identification number.

Each digit is a number from 0 to 9. So, each digit has 10 different choices.

Using the Fundamental Counting Principle (is better than the tree diagram) because it's simpler. To illustrate this, we can attempt to draw a tree diagram.

The first column will be the digits 0 to 9.

Then for each of those digits, we need another 0 to 9.

As you can imagine, the amount of numbers grow exponentially, so using the Fundamental Counting Principle is simpler.

And since we have a 9 digit identification number, with each digit having 10 choices, the total number of identification numbers possible are:

`10* 10* 10 * 10* 10 * 10 * 10 * 10 \time 10* 10=10^9=100000000`

So, 1,000,000,000 identification numbers are possible.