Basic Counting Principle

The Basic or Fundamental Counting Principle can be used determine the possible outcomes when there are two or more characteristics can vary.

Example: Ice cream comes in either a cup or a cone and the flavors available are chocolate, strawberry and vanilla.
                 / chocolate cup
    / chocolate <
   /             \ chocolate cone
  /
 /              / strawberry cup
<-- strawberry <
 \              \ strawberry cone
  \
   \           / vanilla cup
    \ vanilla <
               \ vanilla cone
The diagram above is called a tree diagram and shows all of the possibilities. The tree diagram could also be arranged in another way. Both diagrams have 6 total outcomes.
            / chocolate cup
           / 
    / cup <-- strawberry cup
   /       \ 
  /         \ vanilla cup
 /              
<
 \              
  \          / chocolate cone
   \        / 
    \ cone <-- strawberry cone
            \ 
             \ vanilla cone
							 
To determine the total number of outcomes, multiply the number of possibilities of the first characteristic times the number of possibilities of the second characteristic. In the example above, multiply 3 times 2 to get 6 possible outcomes.
If there are more than two outcomes, continue to multiply the possibilities together to determine the total outcomes.

Find the Total Possible Outcomes

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