MAT 142 Lecture Video SeriesPermutations and CombinationsObjectivesVocabularyFormulasFindList all the combinations of {a, b, c} when the elements are taken two at a time.A group of ten seniors, eight juniors, five sophomores, and five freshmen must select a committee of four.Slide 9Slide 10Slide 11A 7/39 lottery requires choosing seven of the numbers 1 through 39. How many different lottery tickets can you choose? (Order is not important, and numbers do not repeat.)Which Counting Technique?Slide 14Slide 15Creator and Producer Elizabeth Jones for The School of Mathematical and Statistical Sciences at Arizona State University Videographer Mike Jones ©2009 Elizabeth Jones and School of Mathematical and Statistical Sciences at Arizona State UniversityMAT 142Lecture Video SeriesPermutations and CombinationsObjectives•Calculate a permutation. •Calculate a combination. •Determine whether you should use a combination or permutation to calculate the number of outcomes.Vocabulary•combination•permutation•with replacement•without replacementFormulaspermutation!)!(!rrnnCrncombination)!(!rnnPrnwithout replacement andorder is importantwithout replacement andorder is NOT importantnr Find23CFind23PList all the combinations of {a, b, c} when the elements are taken two at a time.A group of ten seniors, eight juniors, five sophomores, and five freshmen must select a committee of four.How many committees are possible if there must be one person from each class on the committee?A group of ten seniors, eight juniors, five sophomores, and five freshmen must select a committee of four.How many committees are possible if there can be any mixture of the classes on the committee?A group of ten seniors, eight juniors, five sophomores, and five freshmen must select a committee of four.How many committees are possible if there must be exactly two seniors on the committee?A group of ten seniors, eight juniors, five sophomores, and five freshmen must select a committee of four.How many committees are possible if the first person chosen is chair of the committee, the second person is secretary, the third person is treasurer and the fourth person is refreshment coordinator?A 7/39 lottery requires choosing seven of the numbers 1 through 39. How many different lottery tickets can you choose? (Order is not important, and numbers do not repeat.)Which Counting Technique?1.What is being selected?2.If the selected items can be repeated, use the Fundamental Principle of Counting and multiply the number of choices for each category.Which Counting Technique?3. If there is only one category, useCombinations if the order of selections does not matter – r is the number of items to be selected from a total of n itemsPermutation if the order of selection does matter – r is the number of items to be selected from a total of n itemsWhich Counting Technique?4. If there is more than one category, use the Fundamental Principle of Counting with one box per category.If you are selecting one item per category, the number in the box for that category is the number of choices for that category.If you are selecting more than one item per category, the number in the box for that category is found by using step 3.Creator and ProducerElizabeth Jones forThe School of Mathematical and Statistical SciencesatArizona State University VideographerMike Jones©2009 Elizabeth Jones and School of Mathematical and Statistical Sciences at Arizona State
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