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The Counting Principle

The Counting Principle. ( ch 8.7 in the textbook) Goal: to use the counting principle to count the number of ways an event can happen. Using the Counting Principle.

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The Counting Principle

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  1. The Counting Principle (ch 8.7 in the textbook) Goal: to use the counting principle to count the number of ways an event can happen

  2. Using the Counting Principle • The Fundamental Counting Principle states that if one event can occur in m ways and another event can occur in n ways, then the two events can occur in mn ways. • Example: • Ice cream comes in either a cup or a cone and the flavors available are chocolate, strawberry and vanilla.

  3. Tree Diagrams • We can also use a tree diagram to find all possible combinations: • Example: Ice cream comes in either a cup or a cone and the flavors available are chocolate, strawberry and vanilla.

  4. Ice cream comes in either a cup or a cone and the flavors available are chocolate, strawberry and vanilla. • 2 x 3 = 6 ways

  5. You go a restaurant to get some breakfast. The menu says pancakes, waffles, or home fries. And for drink, coffee, juice, hot chocolate, and tea. How many different choices of food and drink do you have? • 3 x 4 = 12 choices of food and drink

  6. A nurse has three patients to visit. How many different ways can she make her rounds if she checks each patient once? • 3 x 2 x 1 = 6 ways

  7. High school faculty are to be issued special coded identification cards that consist of four letters of the alphabet. How many different ID cards can be issued if the letters can be used more than once?? • 26 x 26 x 26 x 26 = 456,976 ways

  8. Suppose now that the letters in the high school identification codes cannot be repeated, how many different identification cards can be created? • 26 x 25 x 24 x 23 = 358,800 ways

  9. The digits 0, 1, 2, 3, and 4 are to be used in a 4-digit ID card. How many different cards are possible if repetitions are permitted? • 5 x 5 x 5 x 5 = 625 cards

  10. The digits 0, 1, 2, 3, and 4 are to be used in a 4-digit ID card. How many different cards are possible if repetitions are not permitted? • 5 x 4 x 3 x 2 = 120 cards

  11. Kayla is in charge of a talent show at ACP. There are eight contestants. She must choose in what order they will appear. How many different ways can she schedule the performers? • 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 40,320 ways

  12. Textbook pg. 394 • 1-3; 5-8; 13 • Then: Practice 8.7 WS • HW: Counting Principle HW

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