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Permutations and Combinations

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Objectives Calculate a permutation. Calculate a combination. Determine whether you should use a combination or permutation to calculate the number of outcomes.

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Vocabulary combination permutation with replacement without replacement

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Formulas permutationcombination without replacement and order is important without replacement and order is NOT important

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Find

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List all the combinations of {a, b, c} when the elements are taken two at a time.

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Counting Flow Chart

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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?

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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?

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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?

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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.)

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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.

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Which Counting Technique? 3.If there is only one category, use Combinations if the order of selections does not matter – r is the number of items to be selected from a total of n items Permutation if the order of selection does matter – r is the number of items to be selected from a total of n items

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Which 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.

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