Permutations and Combinations

1
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.

3
Vocabulary

• combination
• permutation
• with replacement
• without replacement

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Formulas

• permutation

combination
without replacement and order is important
without replacement and order is NOT important
5
Find
Find
6
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?
10
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?

• What is being selected?
• 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?

• 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?

• 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.