# Presentation

Presentation

How is data presented,

compared and used to predict

future outcomes?

The standards for this domain…

MM1D1

Students will determine the number of outcomes related to a given event.

MM1D2

Students will use the basic laws of probability.

MM1D3

Students will relate samples to a population.

MM2D1

Using sample data, students will make informal inferences about population

means and standard deviations.

MM2D2

Students will determine an algebraic model to quantify the association between

two quantitative variables.

COUNTING PRINCIPLES – MM1D1

• Multiplication principle

• Permutations & Combinations

Torre is choosing an elective for

his 6 th period class. He can

choose from 2 different band

classes, 3 different computer

classes and 4 different art

classes. How many different

possible choices could Torre

make for his 6 th period class?

Since he can only have one 6th period class the events are

disjoint which means they

have no outcomes in

common.

of counting, there are 2 +3

+ 4 = 9 choices.

Multiplication Principle

An ice cream shop has 24

flavors of ice cream, 8

different toppings, and 3

different types of ice

cream cones. How many

different types of ice

cream cones can be

ordered if each order has

to have a topping, ice

cream, and a cone?

Multiplication Principle

Each order has to have a

cone, a flavor of ice

cream and a topping

so the total number of

choices are

24 · 8 · 3 = 576

TWO MORE TO TRY

Casey is going to buy a car

from Budget Motors, Corner

Motors, or Viking Motors.

Budget Motors sells 10

different models, Corner

Motors sells 8 different

models, and Viking Motors

sells 5 different models of

cars. From how many

different models of cars can

Casey choose?

23

Pete's Pizza offers two

types of crusts: thin crust

or thick crust, and 4

toppings: beef, chicken,

pepperoni, and sausage.

How many different ways

could you order a pizza

with one type of crust and

one topping?

8

Permutations &

Combinations

A permutation is an arrangement in

which the order matters!

A combination is an arrangement in

which order is NOT important!

Factorial n!

Permutations

order matters

If you have 12 pictures and

you want to put 4 of them

on a photo page, how

many different ways can

you choose the pictures for

the photo page?

So you have 12 pictures

choosing 4 at a time.

Permutations

order matters

It is formally written 12P 4

Calculated:

12*11*10*9 =

11,880 ways

Combinations

order does NOT matter

If you have 5 letters

and want to know

how many 2 letter

combinations exist .

Combinations

order does NOT matter

It is formally written 5C 2

Calculated:

5 * 4 = 10

2

TWO MORE TO TRY

There are 8 books on a shelf.

If 3 books are chosen at

random, how many different

groups of 3 books could be

chosen?

56

There are 6 students

qualified to be chosen as

president and vice

president for the Recycle-It

Club. How many different

ways could they be

selected as president and

vice president for the club?

30

“Does order matter?"

QUICK CHECK

A swim team has 12 swimmers who can swim in

a freestyle event. The swim coach will choose

4 of these swimmers for the freestyle relay

race. How can the coach find the number of

possible four-person teams from the eligible

swimmers?

Combination– order does NOT matter.

QUICK CHECK

A swim team has 12 swimmers who can swim in

a freestyle event. The swim coach will choose

4 of these swimmers for the freestyle relay

race. How can the coach determine the

number of different swimmer orders that are

possible for the race?

Permutation – order matters.

QUICK CHECK

A committee must award 3 students with

scholarships. Fifteen students are candidates

for the scholarship including you and your two

best friends. If the awardees are selected

randomly, what is the probability that you and

your two best friends win the scholarships?

Combination– order does NOT matter.

QUICK CHECK

From a group of 5 doctors and 7 nurses, Ellen

must select a committee consisting of 2

doctors and 3 nurses. In how many ways can

she do this?

Combination– order does NOT matter.

QUICK CHECK

How many different ways can Yvonne stack 6

comic books?

Permutation – order matters.

QUICK CHECK

A bag contains 5 cards number 1-5. You draw

one card at a time until you draw all 5 cards.

What is the probability of drawing a card

numbered 1 first and the card numbered 2

second?

Permutation – order matters.

QUICK CHECK

Keisha gets to choose 2 prizes from the grab bag

containing 10 prizes at the Dentist office. How

many ways are 2 prizes possible?

Combination– order does NOT matter.

QUICK CHECK

At a busy restaurant, five tables open up at the

same time. How many different ways can the

hostess seat the next five families waiting to

be seated?

Permutation – order matters.

QUICK CHECK

Debra can choose from 31 flavors of ice cream.

She wants to get a bowl with four different

flavors of ice cream. How many different bowls

of four scoops are possible?

Permutation – order matters.

More Practice

Handout

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