Permutations and CombinationsAdvanced Math Topics

Permutations When a group of objects or people are arranged in a

certain order.

ExampleEight people enter the Best Pie contest. How many ways can

blue, red, and green ribbons be awarded?

Examples Ten people are competing in a swim race where 4

ribbons will be given. How many ways can blue,red, green, and yellow ribbons be awarded?

Permutations with Repetitions

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

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

Combinations An arrangement or selection of objects in which

order is not important

ExampleFive cousins at a family reunion decide that three of

them will go to pick up a pizza. How many ways canthey choose three people to go?

ExampleSix cards are drawn from a standard deck of cards.

How many hands consist of two hearts and four spades?

Example Thirteen cards are drawn from a standard deck of

cards. How many hands consist of six hearts and seven diamonds?

Example A coach must choose five starters from a team of 12 players. 

How many different ways can the coach choose the starters?

Example If 20 people work in a an office and 4 are

selected to go to a conference how many different selections are possible?

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?

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?