PPT-Fundamental Counting Theory, Permutations and Combinations

DM 13 The Fundamental Counting Theory A method for counting outcomes of multistage 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 cways . Mr. Mark Anthony Garcia, M.S.. Mathematics Department. De La Salle University . Experiment: Definition. An . experiment . is a process that generates a set of data. .. Example 1: . Experiment. Tossing of a coin. 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.. 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 . 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.. 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 . 10/14 or 15. Suppose that the numbers of unnecessary procedures recommended by five doctors in a 1-month period are given by the set {2, 2, 8, 20, 33}.. If it is discovered that the fifth doctor recommended an additional 25 unnecessary procedures, how will the median and mean be affected? . 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. Algebra 2. Chapter 10. This Slideshow was developed to accompany the textbook. Larson Algebra 2. By Larson. , R., Boswell, L., . Kanold. , T. D., & Stiff, L. . 2011 . Holt . McDougal. Some examples and diagrams are taken from the textbook.. 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?. Five different stuffed animals are to be placed on a circular display rack in a department store. In how many ways can this be done? .  . 0.07. 72. . 24. . Warm-Up . #. 6 Tuesday, 2/16. Find the number of uni. 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)