Permutations and Combinations

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Permutations and Combinations

• Advanced Math Topics

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Permutations

• When a group of objects or people are arranged in
  a certain order.

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Example

• Eight people enter the Best Pie contest. How many
  ways can blue, red, and green ribbons be awarded?

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Examples

• Ten people are competing in a swim race where
  4ribbons will be given. How many ways can
  blue,red, green, and yellow ribbons be awarded?

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Permutations with Repetitions
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Example

• How many different ways can the letters of the
  word BANANA be arranged?

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Example

• How many different ways can the letters of the
  word ALGEBRA be arranged?

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Combinations

• An arrangement or selection of objects in which
  order is not important

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Example

• Five cousins at a family reunion decide that
  three ofthem will go to pick up a pizza. How
  many ways canthey choose three people to go?

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Example

• Six cards are drawn from a standard deck of
  cards.How many hands consist of two hearts and
  four spades?

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Example

• Thirteen cards are drawn from a standard deck of
  cards. How many hands consist of six hearts and
  seven diamonds?

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Example

• A coach must choose five starters from a team of
  12 players.  How many different ways can the
  coach choose the starters?

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Example

• If 20 people work in a an office and 4 are
  selected to go to a conference how many different
  selections are possible?

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Example

• In gym class Blake is picking a team for tennis,
  he needs to pick 3 people from his class of 20.
  How many different teams could he form?

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Example

• If the Junior class is voting on class officers
  and 8 people have volunteered for the positions
  of President, Vice President, and Historian how
  many ways can the students select their class
  officers?