12.4 Permutations and Combinations

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12.4 Permutations and Combinations

• Objective
• Use Permutations and Combinations

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Factorial

• n!

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Example

• A travel agency is planning a vacation package in
  which travelers will visit 5 cities around
  Europe. How many ways can the agency arrange the
  5 cities along the tour?

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Example

• Lloyd and five friends go to a movie. In how
  many different ways can they sit together in a
  row of 6 empty seats?

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Permutation

• Order is important when arranging items

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Example

• The librarian in the school library is placing 6
  of 10 magazines on a shelf in a school showcase.
  How many ways can se arrange the magazines in the
  case

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Example

• A designer has created 15 outfits and needs to
  select 10 for a fashion show. How many ways can
  the designer arrange the outfits for the show?

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Combination

• Order matters when arranging items.

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Example

• Marques works part-time at a local department
  store. His manager asked him to choose for
  display 5 different styles of shirts from the
  wall of the store that has 8 shirts on it to put
  in a display. How many ways can Marques choose
  the shirts?

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Example

• A group of four students is selecting corsages
  and boutonnieres to wear to the spring dance.
  They choose from 18 different flowers which
  consist of 4 roses, 6 carnations, and 8 tulips.
  In how many ways can 4 flowers be chosen to wear?

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Probability

• A combination lock requires a three-digit code
  made up of the digits 0 through 9. No number can
  be used more than once.
• How many different arrangements are possible
• What is the probability that all of the digits
  are odd numbers?

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Probability

• The Spanish club is electing a president, vice
  president, secretary, and treasurer. Rebecca and
  Lydia are among the nine students who are
  running.
• How many ways can the Spanish club choose their
  officers?
• Assuming that the positions are chosen at random,
  what is the probability that either Rebecca or
  Lydia will be chosen as president or vice
  president?