PPT-Probability-III (Permutations and Combinations)

QSCI 381 Lecture 11 Larson and Farber Sect 34 PermutationsI A is an ordered arrangement of objects The number of different arrangements permutations of n different objects is . 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?. 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 . 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?. 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 . Theoretical Probability. Question #1. Find the theoretical probability . of . rolling . a 2 or 3.. Question #2. A bag contains 36 red, 48 green, . 22 yellow, and . 19 purple blocks. You pick one block from the bag at random. Find the theoretical probability. . 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?. part two. Birthdays. You have a room with . n. people. What is the probability that at least two of them have a birthday on the . same day of the year. ?. Probability model. experiment outcome = birthdays of . 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