May the odds be ever in your favor.

Mechanics

• You should have three (3) official coins. • Get yourself a partner. He/she is your opponent.• When the game starts, you must battle against your opponent

through rock-paper-scissors (also known as jack-en-poy). • For every loss, you must give a coin to the other. For every win, you

must accept a coin from him/her. You must continue the battle until one of you has no more coins to give.

• When you garnered all the coins of your opponent, proceed to battle against the other players.

• The lone winner shall be declared as the Victor.• Happy Hunger Games! And may the odds be ever in your favor.

Post-Hunger Games Questions:

1. In the rock-paper-scissors event, how many possible outcomes can be made by the two players?

Answer: 9

2. In the rock-paper-scissors event, how many possible winning outcomes can be made by the two players?

Answer: 6

3. In the rock-paper-scissors event, how many possible “tabla” outcomes can be made by the two players?

Answer: 3

Essential Question

How is the counting principleapplied to determine outcomes of a certain event?

Objective

Find the total number of outcomes in a sequence of events, using the basic counting rule

Key terms

outcome

•well-defined result

event

•consists of a set of all possible outcomes

tree diagram

•line segment from a starting point to an outcome point

Basic Counting Rule

In a sequence of n events in which the first one has k1 possible outcomes and the second event has k2 and the third has k3, and so forth, the total number of possible outcomes of the sequence will be

k1 ∙ k2 ∙ k3 ∙ ∙ ∙ kn

Counting Rules

Basic Counting

Rule

Permuta-tion

Combina-tion

Examples

• Tossing a Coin and Rolling a Die• Types of Paint• Identification Cards

Tossing a Coin and Rolling a Die

• A coin is tossed and a die is rolled. Find the number of outcomes for the sequence of events.

Tossing a Coin and Rolling a Die

Types of Paint

• A paint manufacturer wishes to manufacture several different paints. The categories include:

How many different kinds of paint can be made if you can select one color, one type, one texture, and one use?

•red, blue, white, black, green, brown, yellow

Color

•latex, oil

Type

•flat, semi-gloss, high gloss

Texture

•outdoor, indoor

Use

Types of Paint

Identification Cards

• The manager of a department store chain wishes to make four-digit identification cards for her employees. How many different cards can be made if she uses the digits 1, 2, 3, 4, 5, and 6 and repetitions are permitted?

Identification Cards

Since there are 4 spaces to fill on each card and there are 6 choices for each space, the total number of cards that can be made is

6 6 6 6 = 1,296

Applications to Science

• Biology• Chemistry• Physics

Biology—Distribution of Blood Types

There are four blood types, A, B, AB, and O. Blood can also be Rh+ and Rh–. Finally, a blood donor can be classified as either male or female. How many different ways can a donor have his or her blood labelled?

Blood Type

A

Rh+M

F

Rh-M

F

B

Rh+M

F

Rh-M

F

AB

Rh+M

F

Rh-M

F

O

Rh+M

F

Rh-M

F

Chemistry—Types of Solutions

A chemistry student wishes to determine the different types of solutions by combining each kind of solute (solid, liquid, gas) to each kind of solvent (solid, liquid, gas). How many different kinds of solutions can be made if he can select one solute and one solvent?

Solution

solid

solid Alloys, coins

liquid Amalgam (Hg, Ag)

gasH2 in

palladium metal

liquid

solid Juicy Pulp

liquid Rubbing alcohol

gas Carbonated drinks

gas

solidCarbon

particles in smoke

liquidH2O

droplets in air

gas air

Physics—Sounds

• Luke has 3 CDs and 3 DVDs with 3 songs recorded in each of them. In how many ways can he play a song?

Number of CDs with Luke = 3 Number of DVDs with Luke = 3 Number of songs in each CD or DVD = 3

Number of ways of playing a song:= 3 × 3 × 3 = 27

Time for Exercises!