Section 12.7

Permutations and Combinations

PermutationsAn arrangement or listing where

order is important.

List the different ways can you arrange these characters?

In how many different ways can you arrange these characters?

Factorials

7! 10! 5!

Travel The Flintstones will visit a complex of theme parks during their summer vacation. They have a four-day pass good at one park per day; they can choose from seven parks. How many different ways can they arrange their vacation schedule?

How many five-digit numbers can be made from the digits 2, 4, 5, 8, and 9 if each digit is used only once?

How many two-digit numbers can be made from the digits 2, 4, 5, 8, and 9 if each digit is used only once?

Track and Field How many ways can six runners be arranged on a four-person relay team?

List different teams of two can you choose from these characters.

Teams:

Combinations

An arrangement or listing

where order is not important.

Shirts How many ways can three shirts be selected from a display having a red shirt, a blue shirt, a green shirt, a black shirt, and a white shirt?

Pens How many ways can a customer choose four pens from a blue, yellow, purple, orange, green, red, or black pen?

Books How many ways can a student select 2 books from a bookshelf containing a mystery, a biography, a non-fiction book, a fantasy book, and a novel?

If all of these characters shake hands, how many handshakes will take place?

How to tell the difference between permutations and combinations:

Does order make a difference?

If yes, then it’s a permutation.

If no, then it’s a combination.

Permutation or Combination?

How many ways can a 3-person team be chosen from 9 people?

How many ways can 15 actors fill 6 roles in a play?

Permutation or Combination?

A pizza shop has 12 toppings to choose from. How many different 3-topping pizzas can be ordered?

Permutation or Combination?

Homework

P 644 10-29 all