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Unformatted text preview: Counting Examples Theorems Examples Fundamental Principle of Counting Theorem (Fundamental Principle of Counting) If the first task has n 1 possible outcomes and the second task has n 2 possible outcomes, then there are n 1 n 2 possible outcomes for the two tasks together. Example Suppose the first task is to roll a fivesided bluecolored die and the second task is to role a sixsided orangecolored die. How many different outcomes are there? Arthur Berg Counting Examples 2/ 12 Theorems Examples Fundamental Principle of Counting Theorem (Fundamental Principle of Counting) If the first task has n 1 possible outcomes and the second task has n 2 possible outcomes, then there are n 1 n 2 possible outcomes for the two tasks together. Example Suppose the first task is to roll a fivesided bluecolored die and the second task is to role a sixsided orangecolored die. How many different outcomes are there? Ans: 6 * 5 = 30. Arthur Berg Counting Examples 2/ 12 Theorems Examples Fundamental Principle of Counting Theorem (Fundamental Principle of Counting) If the first task has n 1 possible outcomes and the second task has n 2 possible outcomes, then there are n 1 n 2 possible outcomes for the two tasks together. Example Suppose the first task is to roll a fivesided bluecolored die and the second task is to role a sixsided orangecolored die. How many different outcomes are there? Ans: 6 * 5 = 30. 1 1 , 1 2 , 1 3 , 1 4 , 1 5 , 1 6 , 2 1 , 2 2 , 2 3 , 2 4 , 2 5 , 2 6 , 3 1 , 3 2 , 3 3 , 3 4 , 3 5 , 3 6 , 4 1 , 4 2 , 4 3 , 4 4 , 4 5 , 4 6 , 5 1 , 5 2 , 5 3 , 5 4 , 5 5 , 5 6 Arthur Berg Counting Examples 2/ 12 Theorems Examples FiveSided Die Arthur Berg Counting Examples 3/ 12 Theorems Examples Two questions to ask Is the order important?...
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 Fall '08
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 Counting, Probability

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