12 2 Permutations Combinations Factorial if n is

12. 2 Permutations & Combinations

Factorial ¡ if n is a positive integer, then n! = n x (n – 1) x (n – 2) x …. Any number with a factorial ! behind it is a

Permutations ¡ When a group of objects or people arranged in a certain order. (order matters) * Also written as n Pr

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

¡ 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 n = total number p & q = the number of times each thing repeats

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

¡ 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 * Also written as n Cr

Examples Five cousins at a family reunion decide that three of them will go to pick up a pizza. How many ways can they choose three people to go?

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

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

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

Mixed Examples: Identify as permutation, permutation w/ rep. or combination ¡ If 20 people work in a an office and 4 are selected to go to a conference how many different selections are possible?

¡ 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?

¡ 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?