PPT-11-1 Permutations and Combinations

111 Permutations and Combinations Holt Algebra 2 Warm Up Lesson Presentation Lesson Quiz Warm Up Evaluate 1 5 4 3 2 1 2 7 6 5 4 3 2 1. Generating Permutations. Many different algorithms have been developed to generate the n! permutations of this set.. We will describe one of these that is based on the . lexicographic . (or . dictionary. 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. Evaluate the following. 6!. MATH 110 Sec 12.3 Permutations and Combinations Practice Exercises . Evaluate the following. 6! = 6 x 5 x 4 x 3 x 2 x 1. MATH 110 Sec 12.3 Permutations and Combinations Practice Exercises . Section 6.. 2. The Pigeonhole Principle. If a flock of . 20. pigeons roosts in a set of . 19 . pigeonholes, one of the pigeonholes must have more than . 1. pigeon.. Pigeonhole Principle. : If . Permutations with Repetition. Theorem 1: . The number of . r-permutations. of a set of . n. objects with repetition allowed is . n. r. . .. Example 1:. How many strings of length . r. can be formed from the English alphabet?. 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?. 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”?. Other Counting Tools: Factorials. MATH 110 Sec 12-3 Lecture: Permutations and Combinations . Other Counting Tools: Factorials. Sometimes we are interested in counting the number of different arrangements of a group of objects.. 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 . Evaluate the following. 6!. MATH 110 Sec 12.3 Permutations and Combinations Practice Exercises . Evaluate the following. 6! = 6 x 5 x 4 x 3 x 2 x 1. MATH 110 Sec 12.3 Permutations and Combinations Practice Exercises . 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 . 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.. Algorithms. a. cademy.zariba.com. 1. Lecture Content. Combinatorics Review. Recursion. Combinatorial Algorithms. Homework. 2. 3. Combinatorics Review. Combinatorics. is a branch of Mathematics concerning the study of finite or countable data structures. Aspects of combinatorics include counting the structures of a given kind and size, deciding when a certain criteria can be met, finding largest/smallest or optimal objects….