PPT-Permutations

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 Bs The concert will feature music by Bach Beethoven Brahms and Bartok In how many different ways can the conductor program each composers music. M408 Probability Unit.  . Example 1 – . a.) How many unique ways are there to arrange the letters PIG?. b.) How many unique ways are there to arrange the letters BOO?.  . To arrange ‘n’ items with. 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. 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. Danny Brown. outline. What is a group?. Symmetry groups. Some more groups. Permutations. Shuffles and bell-ringing. Even more symmetry. Rotation and reflection. Direct and indirect symmetries. what is a group?. 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 . 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?. 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.. 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.. 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 . 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.. 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)