PPT-Counting Permutations

with Repetitions ICS 6D Sandy Irani Permutation Counting How many ways to permute the letters in the word BAD BAD BDA ABD ADB DAB DBA Permutation Counting How many ways to permute the letters in the word ADD. Section 6.3. Section Summary. Permutations. Combinations. Combinatorial Proofs. Permutations. Definition. : A . permutation. of a set of distinct objects is an ordered arrangement of these objects. An ordered arrangement of r elements of a set is called an . Urn models. We are given set of n objects in an urn (don’t ask why it’s called an “. urn. ” - probably due to some statistician years ago) .. We are going to pick (select) r objects from the urn in. Chapter 6. With Question/Answer Animations. Chapter Summary. The Basics of Counting. The Pigeonhole Principle. Permutations and Combinations. Binomial Coefficients and Identities. Generalized Permutations and Combinations. Objective. : . To find the counts of various combinations and permutations, as well as their corresponding probabilities. CHS Statistics. Warm-Up. Alfred . is trying to find an outfit to wear to take Beatrice on their first date to Burger King. How many different ways can he make an outfit out of this following clothes:. Probability. The Fundamental Counting Principle. In this section, you will study several techniques for counting the number of ways an event can occur. One is the Fundamental Counting Principle. You can use this principle to find the number of ways two or more events can occur in sequence.. What is a permutation?. An arrangement of objects or events in which the order is important . . You can use a list to find the number of permutations of a group of objects.. Example #1. The conductor of a symphony orchestra is planning a concert titled “An Evening with the Killer B’s.” The concert will feature music by Bach, Beethoven, Brahms, and Bartok. In how many different ways can the conductor program each composer’s music?. DM. 13. The Fundamental Counting Theory. A method for counting outcomes of multi-stage processes. If you want to perform a series of tasks and the first task can be done in (a) ways, the second can be done in (b) ways, the third can be done in (c) ways, and so on, then all the tasks can be done in a x b x c…ways . M11.E.3.2.1: Determine the number of permutations and/or combinations or apply the fundamental counting principle. Objectives. Permutations. Combinations. Vocabulary. A . permutation. is an arrangement of items in a particular order.. Random Things to Know. Dice. . (singular = “die”). Most cases: 6 sided. Numbers 1,2,3,4,5,6. Special Cases: . 4 sided. 8 sided. 10 sided. 12 sided. 20 sided.  . Random Things to Know. Cards. Typical Deck: 52 cards. AII.12 The student will compute and distinguish between permutations and combinations and use technology for applications. . Fundamental Counting Principle. The Meal Deal at . Bananabee’s. allows you to pick one appetizer, one entrée, and one dessert for $10.99. How many different Meal Deals could you create if you have three appetizers, six entrées, and four desserts to choose from?. Permutations. Objectives. Use the Fundamental Counting Principle to count permutations.. Evaluate factorial expressions.. Use the permutation formula.. Find the number of permutations of duplicate items.. 9/20/2012. 1. Why is counting important?. Recall: the basic definition of the probability of an event, . You need to be able to count how many outcomes fit the event of interest.. You need to be able to count how many outcomes are in the sample space.. Permutations vs. Combinations Warm up- Group Study You have 5 kinds of wrapping paper and 4 different bows. How many different combinations of paper and a bow can you have? Permutation (pg.681 Alg1) Covered in section 6.5 of Rosen’s book. Covered in section 1.4 of . Grimaldi’s. book. Permutations. A . k-permutations . of a set of n objects is the same as a length-k lists. Here the order of the objects is important. .