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Counting Principle:  A method used to compute the number of possible outcomes of an experiment.
The Counting Principle

If an event A can occur in m ways and for each of these m ways, an event B can occur in n ways, then events A and B can occur in ways. This counting principle can be generalized to more than two events that happen in succession. So, if for each of the m and n ways A and B can occur respectively, there is also an event C that can occur in s ways, then events A, B, and C can occur in ways.

Let's suppose that we want to find out how many different license plates are possible, when the license plate is composed of three digits then three letters. To do this you can use the counting principle. The product below gives the number of different plates possible.

We can use this same principle even if there are stipulations on the problem. For example say that a number or letter can only be used once.

What if we wanted to know which plate system provided more possible outcomes, one with five letters or one with seven digits?

 Five letters: Seven digits:

So we see by using the counting principle that there are more possibilities if we use five letters instead of seven digits.