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The Counting Principle

The Counting Principle. Advanced Math Topics. Vocabulary. Independent Events: choice of one thing does NOT affect the choice of another Dependent Events: choice of one thing does affect the choice of another Outcome: the result of a single trial Sample Space: set of all possible outcomes

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The Counting Principle

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  1. The Counting Principle Advanced Math Topics

  2. Vocabulary • Independent Events: choice of one thing does NOT affect the choice of another • Dependent Events: choice of one thing does affect the choice of another • Outcome: the result of a single trial • Sample Space: set of all possible outcomes • Event: one or more outcomes of a trial

  3. The Fundamental Counting Principle • If event M can occur m ways and event N can occur in n ways, then event M followed by event N can occur in mn ways • Basically multiply the number of ways for each event to get the total number of ways the events can occur

  4. Examples • A sandwich cart offers the choice of hamburger, chicken or fish on plain or sesame bun. How many combinations of meat and bun are possible? • Note: meat choice does not affect bun choice so these events are independent

  5. Example: • An ice cream shop offers two types of cones or a bowl, 17 flavors of ice cream, and 40 toppings. How many combinations of one-scoop, one-topping sundaes can you order?

  6. Examples • Kim won a contest on the radio. The prize was a restaurant gift certificate and tickets to a sporting event. She can select one of three restaurants and tickets for football, baseball, basketball, or hockey game. How many different ways can she select a restaurant followed by a sporting event?

  7. Example • A sandwich menu offers customers a choice of white, wheat, or rye bread with one spread chosen from butter, mustard, or mayonaise. How many bread and spread combinations are possible?

  8. *in the blank box of the definitions • Dependent: • If you need to schedule 4 appointments and they are all available in the same four times, how many different appointment schedules could you make?

  9. Example • The Murray’s are choosing a trip to the beach or the mountains. They can travel by car, train, or plane. How many ways can the family select a trip followed by means of transportation?

  10. Example • How many answering machine codes are possible if the code is two digits?

  11. Example • How many license plates can be made if the first three places must be letters and the last three must be numbers?

  12. Examples • How many area codes are possible if each area code is 3-digits?

  13. Examples • How many ATM pin numbers are there if each pin number is 4 characters long and each character could be a number or a letter?

  14. Examples • Charlita wants to take 6 different classes next year. Assuming that each class is offered each period, how many different schedules could she have? • Note if she takes Algebra II first period she won’t take it another period… so this is a dependent event.

  15. Examples • Each player in a board game uses one of six different pieces. If four players play the game, how many different ways could the players choose their game pieces?

  16. Examples • An ice cream shop offers a choice of two types of cones and 15 flavors of ice cream, and the choice of peanuts, chocolate sprinkles, or crushed oreos for toppings. How many different 1-scoop, 1-topping cones can a customer order?

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