# Fundamental Principle of Counting Problem

• LisaL
In summary, the possible combinations for a license plate with three letters followed by three numbers is 15,818,400. However, if we exclude the possibility of all three numbers being zero, the correct number of combinations is 9 x 26 x 26 x 26 x 10 x 10 = 15,818,400.
LisaL

## Homework Statement

A license plate has three letters followed by three numbers. Suppose the digits from 0...9 can be used, except all three digits cannot be zero, and that any letter from A-Z with repeats can be used. How many plates are possible?

## Homework Equations

My question is on the 0. Does this mean NONE can be used or only TWO?

## The Attempt at a Solution

I was marked wrong for the following:

I set up as 26 x 26 x 26 x 10 x 10 x 9 = 15,818,400

What is the correct way to set up this problem?

Thanks!

Ignore the letters for now. If you could have 3 digits with no restrictions, how many numbers can you form? Now if you exclude the possibility of all three being zeros, how many do you have left?

vela said:
Ignore the letters for now. If you could have 3 digits with no restrictions, how many numbers can you form? Now if you exclude the possibility of all three being zeros, how many do you have left?

OK, your point is made. The numbers 000 to 999 not including 000 total nine hundred and ninety nine. On the other hand 10x10x9 seems like it ought to work.

## What is the Fundamental Principle of Counting Problem?

The Fundamental Principle of Counting Problem, also known as the multiplication principle, states that if there are m ways to do one task and n ways to do another task, then there are m x n ways to do both tasks together.

## How is the Fundamental Principle of Counting Problem applied in mathematics?

In mathematics, the Fundamental Principle of Counting Problem is used to calculate the total number of possible outcomes in a given scenario. It is often used in combinatorics and probability problems.

## What is the difference between permutations and combinations in the context of the Fundamental Principle of Counting Problem?

Permutations involve arranging a set of objects in a specific order, while combinations involve selecting a subset of objects without regard to order. Both permutations and combinations use the Fundamental Principle of Counting Problem to calculate the total number of possible outcomes.

## Can the Fundamental Principle of Counting Problem be applied to real-life situations?

Yes, the Fundamental Principle of Counting Problem can be applied to real-life situations such as calculating the number of ways to arrange a set of books on a shelf or the number of ways to choose toppings for a pizza.

## Are there any limitations to the Fundamental Principle of Counting Problem?

The Fundamental Principle of Counting Problem assumes that all outcomes are equally likely. It may not be applicable in situations where certain outcomes are more likely than others.

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