PPT-L14: Permutations, Combinations

L14 Permutations Combinations and S ome R eview EECS 203 Discrete Mathematics Last time we did a number of things Looked at the sum product subtraction and division rules Dont need to know by name. 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.. 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 . and . S. ome . R. eview. EECS 203: Discrete Mathematics. Last time we did a number of things. Looked at the sum, product, subtraction and division rules.. Don’t need to know by name.. Spent a while on the Pigeonhole Principle. 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.. 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 . 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. 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. . 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 . 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. 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)