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Understanding the Fundamental Counting Principle and Tree Diagrams for Combinatorial Problems

This resource provides a comprehensive overview of the Fundamental Counting Principle and its application using tree diagrams. It demonstrates how to calculate the total number of possible outcomes when combining multiple events. For example, with different types of meats, cheeses, and breads, one can calculate the total combinations of sandwiches. The principles extend to dinner choices and license plate combinations. Practical examples illustrate the concepts, enabling learners to master counting techniques in combinatorial mathematics and improve their problem-solving skills.

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Understanding the Fundamental Counting Principle and Tree Diagrams for Combinatorial Problems

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  1. August 9, 2010 Warm-up/Activator Complete the Anticipation Guide.

  2. The Fundamental Counting Principle & Tree Diagrams

  3. The Fundamental Counting Principle • If you have 2 events: 1 event can occur m ways and another event can occur n ways, then the number of ways that both can occur is m*n • Event 1 = 4 types of meats • Event 2 = 3 types of bread • How many different types of sandwiches can you make? • 4*3 = 12

  4. 3 or more events: • 3 events can occur m, n, & p ways, then the number of ways all three can occur is m*n*p • 4 meats • 3 cheeses • 3 breads • How many different sandwiches can you make? • 4*3*3 = 36 sandwiches

  5. At a restaurant at Six Flags, you have the choice of 8 different entrees, 2 different salads, 12 different drinks, & 6 different desserts. • How many different dinners (one choice of each) can you choose? • 8*2*12*6= • 1152 different dinners

  6. Fund. Counting Principal with repetition • Georgia license plates have 3 letters followed by 4 #’s. • How many different licenses plates are possible if digits and letters can be repeated? • There are 10 choices for digits and 26 choices for letters. • 26*26*26*10*10*10*10= • 175,760,000 different plates

  7. Phone numbers • How many different 7 digit phone numbers are possible if the 1st digit cannot be a 0 or 1? • 8*10*10*10*10*10*10= • 8,000,000 different numbers

  8. Tree diagram Flip a coin, then roll a die, list all alternatives

  9. One and Done How many different trucks can you get from three models, four colors and three different engines?

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