Let’s say you had 2 flavors of ice cream (Chocolate, Strawberry), 2 cones (Waffle, Sugar), and 4 toppings (Nuts, M&M’s, Oreo, Butterfinger). Create a tree diagram that represents the combinations of ice cream, cone, and toppings could you make?

Chocolate

Strawberry

Waffle

Sugar

OreoButterfinger

NutsM&M’s

OreoButterfinger

M&M’sNuts

Waffle

Sugar

OreoButterfinger

NutsM&M’s

OreoButterfinger

M&M’sNuts

16 COMBINATIONS IN ALL!!!!

OR

Still 16 Combinations in all !!!!!!

Fundamental Counting PrincipleFundamental Counting Principle

Flavor Cone Topping

2 • 2 • 4= 16 16

Pencils DownPencils Down

Let’s say you had 2 flavors of ice cream (Chocolate, Strawberry), 2 cones (Waffle, Sugar), and 4 toppings (Nuts, M&M’s, Oreo, Butterfinger). How many combinations of ice cream, cone, and toppings could you make? Use a tree diagram

Example:Example:

List all the different orders of the number 1, 2, and 3.

• 1, 2, 3

• 1, 3, 2

• 2, 1, 3

• 2, 3, 1

•3, 1, 2

•3, 2, 1

66 different orders

Tree DiagramTree Diagram

1 2 3

2 3

3 2

1 3

3 1

1 2

2 1

66 different orders

ListList

Example 2:Example 2:

For a combo meal, a fast food chain has a choice 3 main dishes, 2 different sides, and 3 different soft drinks. How many different choices are there?

Tree DiagramTree Diagram

Main1 Main 2 Main 3

Side 1 Side 2

D1 D 2 D 3 D1 D 2 D 3

Side 1 Side 2

D1 D 2 D 3 D1 D 2 D 3

Side 1 Side 2

D1 D 2 D 3 D1 D 2 D 3

1818 different orders

Example 2:Example 2:

For a combo meal, a fast food chain has a choice 3 main dishes, 2 different sides, and 3 different soft drinks. How many different choices are there?

Fundamental Counting PrincipleFundamental Counting Principle

Main Dishes

Sides Soft Drinks

3 • 2 • 3 = 18 18 different orders

Example 3:Example 3:

A network executive has 2 suits, 4 shirts, 3 ties, and 2 pairs of shoes. How many different combinations of one suit, one shirt, one tie and one pair of shoes can he choose?

Fundamental Counting PrincipleFundamental Counting Principle

Suits Shirts Ties

2 • 4 • 3Shoes

• 2= 48 48 different combos!

Ten boys were nominated for Homecoming King and four girls have been nominated for Homecoming Queen and Princess. How many different courts are possible?

King Queen Princess

10 • 4 • 3= 120 120 different possibilities

Seven boys and five girls are running for President, Vice-President and Secretary at their school. However, the girls are only running for President and the boys are not running for President. How many different ways can the students be elected?

President

Vice-President

Secretary

5 • 7 • 6= 210 210 different combinations

Example 2:Example 2:How many different license plates can be manufactured if the configuration is 3 letters (from A to Z) followed by four digits (from 0 to 9) with no repeats?

CaliforniaMarch 2011Given the write type of equation, students can solve by thinking analytically.

1st Letter 2nd Letter

3rd Letter 1st Number

2nd Number

3rd Number

2626 •• 2525 •• 2424 •• 1010 •• 99 •• 88

= 78,624,000 78,624,000 different ways

4th Number

•• 77

26 Letters 10 Numbers

You try:You try:The computer network administrator has asked JOHN to create 8-character password. He must use the arrangements of the 4 letters of his first name JOHN, followed by the arrangements of the 4 numbers in the year he was born, 1985. How many different passwords could he create?

1st Letter 2nd Letter

3rd Letter 4th Letter

1st Number

2nd Number

44 •• 33 •• 22 •• 11 •• 44 •• 333rd

Number

•• 224th

Number

•• 11

= 576 576 different passwords