Permutations and
Combinations
Advanced Math Topics
Permutations

When a group of objects or people are arranged in a
certain order.
Example
Eight 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
Example
How 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
Example
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?
Example
Six 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?