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Introductory Statistics Lesson 3.4 A Objective: SSBAT determine the number of permutations. Standards: M11.E.3.2.1
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Permutation An arrangement of data where order is IMPORTANT ABC is not the same as CBA Can use the Fundamental Counting Principle to find Can also find the number of different permutations of n distinct objects using n!
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n! Read as n factorial Defined as: n! = n(n – 1)(n – 2) (n – 3) ···3·2·1 Examples: 5! 9! = 5 · 4 · 3 · 2 · 1 = 120 = 9 · 8 · 7 · 6 · 5 · 4 · 3 · 2 · 1 = 362,880
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There is a factorial key on the calculator Go to MATH Scroll over to PRB Then choose #4 which is ! Practice: 8! 12! 10! – 4! = 40,320 = 479,001,600 = 3,628,776
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Example: Find the number of ways 6 people can finish a race. Method 1: Fundamental Counting Principle 6 · 5 · 4 · 3 · 2 · 1 = 720 Method 2: Permutation 6! = 720
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Answer: 840 Answer: 99,638,080,820,000
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2.The board of directors for a company has 12 members. One member is the president, another is the vice-president, another is the secretary, and another is the treasurer. How many ways can these positions be assigned?
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3.A museum is going to hang 9 paintings on a wall from left to right. How many different ways can the museum hang these 9 paintings on the wall?
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Complete Worksheet 3.4 A
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