PPT-6-7 Permutations & Combinations

M11E321 Determine the number of permutations andor combinations or apply the fundamental counting principle Objectives Permutations Combinations Vocabulary A permutation is an arrangement of items in a particular order. 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. 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 . 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. Objective. : . To find the counts of various combinations and permutations, as well as their corresponding probabilities. CHS Statistics. Warm-Up. Alfred . is trying to find an outfit to wear to take Beatrice on their first date to Burger King. How many different ways can he make an outfit out of this following clothes:. 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 Subsets. ICS 6D. Sandy . Irani. Lexicographic Order. S a set. S. n . is the set of all n-tuples whose entries are elements in S.. If S is ordered, then we can define an ordering on the n-tuples of S called the . 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”?. 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. . 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 . 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.