1. 12-6 Combinations
Goal:
Use Combinations to count the number of ways an event can happen.

2. Vocabulary Combinations:
The number of ways objects can be put into a group.
Symbol: nCr OR C(n,r)
Formula:
n is the total number of items (bigger #)
r is the number being put in the group (smaller #)
On Calculator: MATH  PRB  nCr

3. Examples
How many groups of 3 students could I create in this classroom?
There is a group of 50 workers and only 8 are going to attend a conference. How many groups could attend the conference?
There are 10 women and 8 men in a club. How many groups of 3 could be created?
536,878,650
816

4. Examples
There are 52 cards in a deck. How many different 5 card hands could be dealt?
There are 15 books on a summer reading list. If you only have to read 5 books, how many different groups of 5 could you read?
2,598,960
3003

5. Jacky is packing for her vacation to the mountains
Jacky is packing for her vacation to the mountains. With all her heavy snow gear, she only has room left for 4 more outfits to wear. If she has 7 different outfits laid out on the bed, how many ways can the 4 outfits be chosen?
A. 35
B. 840
C. 148
D. 46

6. Practice
Worksheet – “Combinations”

7. Donut Shop How many different donuts can be created with:
Fillings
Toppings
Jelly
Sprinkles
Cream
Chocolate Frosting
Chocolate Cream
Vanilla Frosting
Boston Cream
Glaze
Powder
How many different donuts can be created with:
1 filling and 1 topping?
Jelly and 3 toppings?
Chocolate Cream and 4 toppings?
2 toppings and any filling? 20 10 5 40

8. Ice Cream Shop How many different ice creams can be created with:
Flavors
Toppings
Chocolate
Chocolate Syrup
Vanilla
Peanut Butter
Mint Chocolate Chip
Caramel
Coffee
Nuts
Strawberry
Sprinkles
M & M’s
How many different ice creams can be created with:
Chocolate ice cream and 3 toppings?
Strawberry ice cream and 2 toppings?
3 toppings and any flavor?
4 toppings and any flavor? 20 15
120 90

9. A teacher assigns the order of five students who are giving presentations today. Identify the situation as a permutation or a combination.
A. permutation
B. combination

10. Practice telling the difference between Permutations and Combinations
Page #2-4, 20-24

11. Homework
Worksheet – “12-6 Counting Principle, Permutation and Combinations Homework”