Warm-up

What is the probability that you will pick one card that is a number 12 out of a regular deck of playing cards?

What is the probability that you will pick an even number out of the numbers 2, 4, 6, 8, 10?

Counting PrinciplePermutationsCombinations

After today, you will be able to count outcomes, use

permutations, and use combinations.

Bagel Mania!

Bagel Mania offers chicken, tuna, and vegetable sandwiches on plain or onion bagels. How many possible sandwiches are there?

Tree Diagram

Chicken Tuna Vegetable

Plain Onion PlainPlain OnionOnion

Counting Principle

To find the total number of outcomes, multiply your options together.

EX) 8 different pizza toppings and 3 types of crust (stuffed, thick, thin). How many different combinations for a one-topping pizza?

EX) Four coins are tossed.

How many different ways can you order an ice cream if the choices are:

What is the probability the ice cream will be in a sugar cone?

Type of cone Number of scoops

Ice cream flavor

Toppings

Sugar or waffle One or two Chocolate, vanilla, coffee or pistachio

Sprinkles, syrup, or none

Permutations

Permutation- an arrangement or listing in which order is important.

How many arrangements are possible with a 4-swimmer relay? 4 x 3 x 2 x 1 or 4P4 in your calculator

How many arrangements are possible with 5 swimmers for a 4-swimmer relay? 5 x 4 x 3 x 2 or 5P4 in your calculator

Permutations

Find P(8,3) P(8,3) means the number of orders of 8 things

taken 3 at a time.

Combinations

Combination- arrangements where order is NOT important.

Examples:

Combinations

Ex) In gym class Mr. Merrill picked 10 students to compete in the 100m dash. The top three finishers each received a free t-shirt. How many combinations of winners could there be?

Permutation OR Combination?

Four books in a row 6 CDs from a group of 20 A team of 6 players from 12 Ten people in line to buy tickets

Permutations

What is 4! 4! Is read as “four factorial”

Find 6!