4.2 Permutations

Apr 07, 2014

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4.2 Permutations

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Permutations

A permutation is an arrangement of a set of objects for which the order of the objects is important.. Show the number of ways of arranging the letters of the word CAT:. CATCTAACTATCTCATAC. . There are six arrangements or permutations ofthe word CAT. By changing the order of the letters, you have a different permutation..

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Permutations

Permutations. Jessica O’Donnell. Math Journal: Permutations: Arrangements where the order matters. It would be like the runners in a race. Who will come in first, second, or third?. How many different ways could they be put in order?. Sally. Sally. Sally. Sally. Sally. Sally. Cheetah.

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Permutations

Permutations. Objectives: Solve problems involving linear permutations of distinct or indistinguishable objects. Solve problems involving circular permutations. Standards: 2.7.8A Determine the number of permutations for an event. A permutation is an arrangement of objects

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Permutations

Permutations. Factorials. How can we arrange 5 students in a line to go to lunch today?. _________ __________ __________ __________ ________. Factorials. Definition: The product of integers from 1 to n. For Example: How many ways can I arrange the letters in the word APRIL ?.

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Permutations

Chapter 7 Combinatorics. 7.2. Permutations. 7.2. 1. MATHPOWER TM 12, WESTERN EDITION. Permutations. A permutation is an arrangement of a set of objects for which the order of the objects is important. Show the number of ways of arranging the letters of the word CAT :. CAT CTA

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Permutations

Permutations. Definition of Permutation. An arrangement of objects in which the order of selection matters. Ex: You have to visit Andrew’s house (A), Betty’s house (B), and Carlos’ house (C) but you have not decided the order. What are the different ways you can visit all 3 houses? .

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Permutations

9! = 9 • 8 • 7 • 6 • 5 • 4 • 3 • 2 • 1 = 362,880. Simplify. COURSE 3 LESSON 11-2. Permutations. A CD has nine songs. In how many different orders could you play these songs?. The songs can be played in 362,880 different orders or permutations. 11-2.

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PERMUTATIONS

PERMUTATIONS. Permutation. Method of counting when order matters Example: Coming in first, second, or third Combination locks. Examples. How many ways can 5 students be arranged in 5 desks? There are 5 choices for the first desk, 4 for the second, 3 for the third, etc. Examples.

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Permutations

Permutations. S10.2. Lesson Objectives. Use the Fundamental Counting Principle to determine the number of outcomes in a problem. Use the idea of permutations to count the number of possible outcomes in a problem. Fundamental Counting Theorem.

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10.2 Permutations

10.2 Permutations. Objectives: Solve problems involving linear permutations of distinct or indistinguishable objects. Solve problems involving circular permutations. Standards: 2.7.8A Determine the number of permutations for an event. A permutation is an arrangement of objects

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Permutations Examples

Permutations Examples. 1. How many different starting rotations could you make with 6 volleyball players? (Positioning matters in a rotation.). Permutations Examples. 6 •5•4•3•2•1 = 6! = 720

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Permutations

Permutations. Basics. 5!. Does not mean FIVE!. 5! is read five factorial. 5!. = 5 • 4 • 3 • 2 • 1. 7!. = 7 • 6 •5 • 4 • 3 • 2 • 1. 5! = 120. 7! = 5040. When a group of objects or things are arranged in a certain order, the arrangement is called a permutation.

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PERMUTATIONS

COUNTING TECHNIQUES. PERMUTATIONS. AND. COMBINATIONS. Computer Science, Statistics and Probability all involve counting techniques which are a branch of mathematics called combinatorics (ways to combine things). We'll be introducing this topic in this section.

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Permutations

Permutations. Permutations. Objectives : (1) Students will be able to use permutations to find all possible arrangements involving a limited number of choices. Essential Questions : (1) What are permutations and how can we find them?. Permutations. What is a Permutation ?

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4.2 Permutations of sets

4.2 Permutations of sets. 4.2.1 Basic counting principles Theorem 4.3(Addition principle): If A 1 , A 2 , … , A n are disjoint sets, then the number of elements in the union of these sets is the sum of the numbers of elements in them. | A 1 ∪A 2 ∪…∪A n |=|A 1 |+|A 2 |+…+|A n |.

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Permutations

Permutations. Introduction – Lecture 2. Permutations. As we know a permutation p is a bijective bijektivna mapping of a set A onto itself: p : A  A. Permutations may be multiplied and form the symmetric group Sym(A) = S A , that has n! elements, where n = |A|.

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Permutations

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Permutations

Permutations. Warm Up – Find the Mean and the Standard Deviation. Warm Up – Find the Mean and Standard Deviation. Objective. Find Sample Space using Permutations and Combinations. Relevance.

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