Basic Principles of Counting
|
|
Introduction
|
|
Counting is a simple mathematical principle that can be used to solve many real world problems that arise in everyday life. It also provides some basic understanding that is needed to understand more complex ideas that you will learn later on. The first basic principle of counting is the sum rule.
|
The Sum Rule
|
|
The sum rule states that "if a task can be done in 'm' ways and a second task can be done in 'n' ways, and if these tasks cannot be done at the same time, then there are 'm + n' ways to do either task." |
|
|
Example 1: |
A student can choose a computer science project from one of four lists. The four lists contain 14, 33, 29, and 20 possible projects, respectively. How many possible projects are there to choose from? |
|
Solution
|
|
Example 2: |
Suppose Michael has to do a report on either a US Senator or a US Representative. How many different reports does Michael have to choose from? (Note - there were 100 Senators and 435 Representatives at the time this tutorial site was created) |
|
Solution |
|
The Product Rule
|
|
The second basic principle of counting is the Product Rule. The product rule states that "if a procedure can be broken down into two tasks, and there are 'm' ways to do the first task and 'n' ways to do the second task, then there are 'm * n' ways to do the procedure. |
|
|
Example 1: |
Suppose that Michael has to do a report on either the geographical features, history, or tourist attractions of any state in America. Because there are 50 states, and three different possible reports for each state, there are 150 (50 * 3 = 150) possible reports to choose from.
|
|
Example 2: |
There are 32 computers in a computer lab. Each computer has 5 ports. How many different ports to a computer are there in the lab? |
|
|
Solution
|
|
Example 3: |
How many different license plates are available if each plate contains a sequence of three letters followed by four digits? |
|
|
Solution |
Now that you have learned the two most basic principles of counting, click on the 'next page' link below to learn about more principles of counting. |