Exploration - Permutation Suppose that a manager of a softball team is filling out her team’s lineup card before the game, the order in which the names are filled out is important as it determines the order which the players will bat. Suppose that she has 7 possible players in mind for the top 4 spots in the lineup. How many different ways can the manager fill in the line up?

Exploration - Permutation Suppose that a manager of a softball team is filling out her team’s lineup card before the game, the order in which the names are filled out is important as it determines the order which the players will bat. Suppose that she has 7 possible players in mind for the top 4 spots in the lineup. How many different ways can the manager fill in the line up? __________________________________ First Second Third FourthTotal

Exploration - Permutation Suppose that a manager of a softball team is filling out her team’s lineup card before the game, the order in which the names are filled out is important as it determines the order which the players will bat. Suppose that she has 7 possible players in mind for the top 4 spots in the lineup. How many different ways can the manager fill in the line up? __________________________________ First Second Third FourthTotal

Permutations – Definition

Permutations

Example – Figure Skating There are 7 finalist for the world championship of skating. How many ways can gold, silver and bronze medals be awarded?

Example – Figure Skating There are 7 finalist for the world championship of skating. How many ways can gold, silver and bronze medals be awarded? Does order matter?

Example – Figure Skating There are 7 finalist for the world championship of skating. How many ways can gold, silver and bronze medals be awarded? Does order matter? YES!!! This is a permutation.

Example – Figure Skating

Permutations with Repetition

# of P # of O # of Y

Permutations with Repetition # of P # of O # of Y

Permutations with Repetition # of P # of O # of Y

Permutations with Repetition # of P # of O # of Y

Permutations with Repetition How many distinct permutations of the word MAMA exist? Of the word MISSISSIPPI?

Permutations with Repetition

CW 12.2 – Permutations