Basic Counting Principle

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Basic Counting Principle: Learn

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

Example: Ice cream comes in either a cup or a cone and the flavors available are chocolate, strawberry and vanilla.

  • Vanilla
    • Vanilla Cone
    • Vanilla Cup
  • Chocolate
    • Chocolate Cone
    • Chocolate Cup
  • Strawberry
    • Strawberry Cone
    • Strawberry Cup

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.

  • Cone
    • Vanilla Cone
    • Chocolate Cone
    • Strawberry Cone
  • Cup
    • Vanilla Cup
    • Chocolate Cup
    • Strawberry Cup

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 characteristics, continue to multiply the possibilities together to determine the total outcomes.

Basic Counting Principle: Practice

Find the total possible outcomes.

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How fast can you get 20 more correct answers than wrong answers? 999

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