Permutations and Combinations Page 1 of 2 Permutations and Combinations Objectives: • 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 replacement =rnC =rnP 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. 3. If there is only one category, use: • combinations if the order of selections does not matter – that is, r items can be selected from a pool of n items in !)!(!rrnnCrn−= ways. • permutation if the order of selection does matter – that is r items cam be selected from a pool of n items in )!(!rnnPrn−= ways. 4. If there is more than one category, use the Fundamental Principle of Counting with one box per category. a. If you are selecting one item per category, the number in the box for that category is the number of choices for that category. b. If you are selecting more than one item per category, the number in the box for that category is found by using step 3.Permutations and Combinations Page 2 of 2 Possible Classroom Examples: Find 23C. List 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 the committee must contain the following? a. one person from each class b. any mixture of the classes c. exactly two seniors How many five-card poker hands consisting of three kings and two queens are possible? How many five-card poker hands consisting of three of a kind and a pair (a full house) are possible? 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 the numbers do not
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