let’s say you had 2 flavors of ice cream (chocolate, strawberry), 2 cones (waffle, sugar), and 4...
TRANSCRIPT
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