PPT-5.3 Permutations and Combinations

Urn models We are given set of n objects in an urn dont ask why its called an urn probably due to some statistician years ago We are going to pick select r objects from the urn in. Definition of Combination. An . arrangement. . of objects in which the . order. . of selection . does NOT matter. .. . Ex: You have to visit three out of your four friends houses: Andrew (A), Betty (B), Carlos (C), Dave (D). What are the different ways to select the 3 houses to visit?. 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?. 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. 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.. Section . 6.5. Permutations with Repetition. Theorem . 1. : The number of . r. -permutations of a set of . n. objects with repetition allowed is . n. r. .. . Example. : How many strings of length . One make of cellular telephone comes in 3 models. Each model comes in two colors (dark green and white). If the store wants to display each model in each color, how many cellular telephones must be displayed? Make a tree diagram showing the outcomes for selecting a model and a color.. 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”?. 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. 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 . Discrete Structures, Fall 2011. Permutation . vs. Combination. Permutations. Combinations. Ordering of elements from a set. Sequence does matter. 1 2 3 is not the same as 3 2 1. Collection of element from a set. 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?. 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…. 11-1 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