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13.3 The Fundamental Counting Principle

13.3 The Fundamental Counting Principle. Objectives: Use tree diagrams to count the number of choices that can be made from sets. Use the Fundamental Counting Principle to count the number of choices that can be made from sets.

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13.3 The Fundamental Counting Principle

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  1. 13.3 The Fundamental Counting Principle Objectives: Use tree diagrams to count the number of choices that can be made from sets. Use the Fundamental Counting Principle to count the number of choices that can be made from sets. Standard Addressed: 2.7.11 D: Use theoretical probability distributions to make judgments about the likelihood of various outcomes in uncertain situations.

  2. Ex. 1 a. Use a tree diagram to find the number of elective pairs that are possible for Abby. She may choose one elective from cluster 1 (band or orchestra or chorus) and one from cluster 2 (home economics or woodworking).

  3. 1b. A diner at a café may select 1 of 6 main dishes and 1 of 2 desserts. Use a tree diagram to find how many different meals are possible. • Chicken – vanilla or chocolate • Beef – vanilla or chocolate • Pork – vanilla or chocolate • Turkey – vanilla or chocolate • Pasta – vanilla or chocolate • Salad – vanilla or chocolate • 12 possiblities

  4. Fundamental Counting Principle: If there are m ways that one event can occur andnways that another event can occur, then there are m x n ways that both events canoccur. Tree diagrams illustrate the fundamental counting principle.

  5. Ex. 2a.

  6. Ex. 2b. A car buyer can choose one of three different models of a new car. Five different colors are available for each. How many ways can the buyer make the choices? Relate your answer to the Fundamental Counting Principle. 3 * 5 = 15 ways

  7. Ex. 3 Ann is choosing a password for her access to the Internet. She decides not to use the digit 0 or the letter O. How many passwords of 2 letters followed by 4 digits are possible? • 25 letters and 9 digits • 25 * 25 * 9 * 9 * 9 * 9 = 4,100,625

  8. Ex. 4a.

  9. Ex. 4b. Jacob is selecting color pens. The first characteristic is the point, which may be either felt tip or ball-point. The second characteristic is the color – red, blue, green, or black. The third characteristic is the brand – Able or Blakely. How many possible selections of a pen can Jacob make? 2 * 4 * 2 = 16

  10. Ex. 5

  11. Fundamental Counting Principle and Probability • Ex 6. A license plate consists of 2 letters followed by 3 digits. The letters, A-Z, and the numbers, 0-9, can be repeated. Find the probability that your new license plate contains the initials of your first and last names in their proper order.

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