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# Using the Counting Principle in Probability Theory

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A mini license plate for a toy car must consist of a letter followed by two numbers. Each letter must be a C, A or R. Each number must be a 3 or 7. Repetition of digits is permitted.

a) Use the counting principle to determine the number of points in the sample space.

b) Describe how a tree diagram would represent this situation.

c) List the sample space.

d) Determine the exact probability of creating a mini license plate with a 7. Give solution exactly in reduced fraction form.

##### Solution Summary

This solution shows how to apply the counting principle in probability theory to determine the number of points in a sample space.

##### Solution Preview

a) Possibilities for the first character: 3
Second character: 2
Third character: 2
The total number of points in the sample space is 3*2*2 = 12 ...

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