PPT-5.5 Generalized Permutations and Combinations

Permutations with Repetition Theorem 1 The number of rpermutations 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. 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 . 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. 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 . 6.5. 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 . Evaluate the following. (7-3)! . 6! . MATH 110 Sec 12.3 Permutations and Combinations Practice Exercises . Evaluate the following. . = . . . = . . .  .  . . MATH 110 Sec 12.3 Permutations and Combinations Practice Exercises . 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.. 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.. Discrete Structures, Fall 2011. Permutation . vs. Combination. Permutations. Combinations. Ordering of elements from a set. Sequence does matter. 1 2 3 is not the same as 3 2 1. Collection of element from a set. 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) 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