1. Creating Combinations
Determine the sample space (set of possible outcomes) for a given experiment and determine which members of the sample space are related to certain events. Sample space may be determined by the use of tree diagrams, tables, or pictorial representations.

2. Finding Outcomes 13.2 Notes Methods Tree Diagram Table Organized List
Combinations – Order is NOT important
Permutations– Order is important
Methods
Tree Diagram
Table
Organized List

3. I can… Self Assessment Use tree diagrams to find outcomes
Use tables or lists to find outcomes
Self Assessment
5- I can do it without help & teach others.
4- I can do this with no help, but I don’t know if I can explain it.
3- I can do this with a little help.
2- I can do this with a lot of help!
1- I don’t have a clue.

4. What are creating combination problems?
Creating combination problems are stories that ask you to find
all the possible matches, combinations, pairs, or outecomes that
can be made out of a group of objects.

5. For example, we have all seen problems like this:
Suzanne has a red shirt, a blue shirt, and a pink shirt. She also
has a pair of black pants and a pair of gray pants.
How many different ways can Suzanne wear one shirt and
one pair of pants?

6. x Wrong Answer! There’s the outfit I like. I’m done. Some students
It is important to remember that you are not just making one outfit
for Suzanne, but you are finding all the different outfits she could
wear. You are determining all the different ways she could match up
the shirts she has with the pants she has.
There’s the outfit
I like. I’m done.
Some students
make the mistake
of putting just
the answer they
like best and not
finishing the
problem.
Wrong Answer!

7. Don’t be tricked by the word “one” in the problem. That doesn’t
mean make only one outfit. That just means Suzanne can only wear
one shirt with one pair of pants at a time. Don’t try to dress her in
three shirt and two pants all at once. That would look pretty silly!!!

8. red shirt with black pants blue shirt with black pants
So, how do we find out how many outfits Suzanne has
to choose from?
There is an easy way and a hard way.
The hard way is to just randomly match up shirts and
pants, write them down, and hope we find them all
without accidentally repeating any.
red shirt with black pants
blue shirt with black pants
pink shirt with gray pants

9. ? ? ? ? ? ? ? ? ? But how do we know for certain that
we have found all the possible
combinations or matches? ? ? ? ? ?

10. The Easy Way!! The hard way can get pretty confusing and it can take
a long time to figure out.
But….
Smart mathematicians know
The Easy Way!!

11. red shirt black pants blue shirt gray pants pink shirt
The easy method is called a Tree Diagram.
Step 1: Make simple lists of the items you are matching.
red shirt
blue shirt
pink shirt
black pants
gray pants

12. black pants red shirt gray pants black pants blue shirt gray pants
Step 2: Build your trees. The first list will be the trunks and
the second list is the branches.
Suzanne can wear
her red shirt with
the black pants or
she can wear the
red shirt with her
gray pants. So far
that’s 2 different
combinations.
black pants
red shirt
gray pants
black pants
blue shirt
2 more
gray pants
black pants
And 2 more.
pink shirt
gray pants
6 outfits in all!

13. 3 shirts that can be worn with 2 pants each = 6 outfits
Suzanne can use her three shirts
and two pairs of pants
to make six different outfits.
3 shirts that can be worn with 2 pants each = 6 outfits
3 x 2 = 6

14. Example 2 – a fair coin is flipped twice, what are all the possible outcomes?
1st
2nd H HH
Possible Outcomes H T HT H TH T T TT

15. Example 3 – Your art class is painting pottery for an art fair
Example 3 – Your art class is painting pottery for an art fair. You can choose a small or a large size and you can paint a vase, a jar, or a plate, What are the different kids of pottery you can paint?
Step 1: List the sizes S L

16. Step 2: List the items for each size
Example 3 – Your art class is painting pottery for an art fair. You can choose a small or a large size, and you can paint a vase, a jar, or a plate, What are the different kids of pottery you can paint?
Step 2: List the items for each size V J S P V L J P

17. Step 2: Find the Outcomes
Example 3 – Your art class is painting pottery for an art fair. You can choose a small or a large size, and you can paint a vase, a jar, or a plate, What are the different kids of pottery you can paint?
Step 2: Find the Outcomes V SV
Possible Outcomes J SJ S P SP V LV L J LJ P PT

18. Your Turn– A roller hockey team is choosing jerseys
Your Turn– A roller hockey team is choosing jerseys. The body can be red, white, purple, or green. The sleeves can be black, red, or blue. List all the possible jerseys that the team can choose.
Red Black
Black R
Red
Red Red
Blue
Red Blue
Black
White Black W
White Red
Red
Blue
White Blue
Possible Outcomes
Black
Purple Black P
Red
Purple Red
Purple Blue
Blue
Green Black
Black
Green Red G
Red
Green Blue
Blue

19. Combinations vs. Permutations
Combination  group of objects in which order is NOT important
Example: Choosing 2 pizza toppings from a list of 5 or flipping a coin
Permutation  group of objects in which order is important
Example: Order of doing chores or finding all of the digit numbers from a list of 5 digits

20. Are you finding an combination or a permutation?
Using a table
You can choose 2 toppings for a sundae from nuts, sprinkles, caramel, and marshmallows. Find all the possible pairs of toppings.
Are you finding an combination or a permutation?
It doesn’t matter which topping is selected first.

21. Using a table
You can choose 2 toppings for a sundae from nuts, sprinkles, caramel, and marshmallows. Find all the possible pairs of toppings.
Nuts
Sprinkles
Caramel
Marshmallows
Outcomes

22. Using a table
You can choose 2 toppings for a sundae from nuts, sprinkles, caramel, and marshmallows. Find all the possible pairs of toppings.
Nuts
Sprinkles
Caramel
Marshmallows
Outcomes X
NUTS, SPRINKLES

23. Using a table
You can choose 2 toppings for a sundae from nuts, sprinkles, caramel, and marshmallows. Find all the possible pairs of toppings.
Nuts
Sprinkles
Caramel
Marshmallows
Outcomes X
NUTS, SPRINKLES
NUTS, CARAMEL

24. Using a table
You can choose 2 toppings for a sundae from nuts, sprinkles, caramel, and marshmallows. Find all the possible pairs of toppings.
Nuts
Sprinkles
Caramel
Marshmallows
Outcomes X
NUTS, SPRINKLES
NUTS, CARAMEL
NUTS, MARSHMALLOW

25. Using a table
You can choose 2 toppings for a sundae from nuts, sprinkles, caramel, and marshmallows. Find all the possible pairs of toppings.
Nuts
Sprinkles
Caramel
Marshmallows
Outcomes X
NUTS, SPRINKLES
NUTS, CARAMEL
NUTS, MARSHMALLOW
SPRINKLES, CARAMEL

26. SPRINKLES, MARSHMALLOW
Using a table
You can choose 2 toppings for a sundae from nuts, sprinkles, caramel, and marshmallows. Find all the possible pairs of toppings.
Nuts
Sprinkles
Caramel
Marshmallows
Outcomes X
NUTS, SPRINKLES
NUTS, CARAMEL
NUTS, MARSHMALLOW
SPRINKLES, CARAMEL
SPRINKLES, MARSHMALLOW

27. SPRINKLES, MARSHMALLOW
Using a table
You can choose 2 toppings for a sundae from nuts, sprinkles, caramel, and marshmallows. Find all the possible pairs of toppings.
Nuts
Sprinkles
Caramel
Marshmallows
Outcomes X
NUTS, SPRINKLES
NUTS, CARAMEL
NUTS, MARSHMALLOW
SPRINKLES, CARAMEL
SPRINKLES, MARSHMALLOW
CARAMEL, MARSHMALLOW

28. Your Turn
You can choose 2 vegetables for a stir-fry from green peppers, pea pods, onions, and broccoli. List all the possible pairs of vegetables.
Green peppers
Pea pods
Onions
Broccoli
Outcomes

29. Your Turn
You can choose 2 vegetables for a stir-fry from green peppers, pea pods, onions, and broccoli. List all the possible pairs of vegetables.
Green peppers
Pea pods
Onions
Broccoli
Outcomes X
Green pepper, pea pod

30. Your Turn
You can choose 2 vegetables for a stir-fry from green peppers, pea pods, onions, and broccoli. List all the possible pairs of vegetables.
Green peppers
Pea pods
Onions
Broccoli
Outcomes X
Green pepper, pea pod
Green pepper, onions

31. Your Turn
You can choose 2 vegetables for a stir-fry from green peppers, pea pods, onions, and broccoli. List all the possible pairs of vegetables.
Green peppers
Pea pods
Onions
Broccoli
Outcomes X
Green pepper, pea pod
Green pepper, onions
Green pepper, broccoli

32. Your Turn
You can choose 2 vegetables for a stir-fry from green peppers, pea pods, onions, and broccoli. List all the possible pairs of vegetables.
Green peppers
Pea pods
Onions
Broccoli
Outcomes X
Green pepper, pea pod
Green pepper, onions
Green pepper, broccoli
Pea pods, onion

33. Your Turn
You can choose 2 vegetables for a stir-fry from green peppers, pea pods, onions, and broccoli. List all the possible pairs of vegetables.
Green peppers
Pea pods
Onions
Broccoli
Outcomes X
Green pepper, pea pod
Green pepper, onions
Green pepper, broccoli
Pea pods, onion
Pea pods, broccoli

34. Your Turn
You can choose 2 vegetables for a stir-fry from green peppers, pea pods, onions, and broccoli. List all the possible pairs of vegetables.
Green peppers
Pea pods
Onions
Broccoli
Outcomes X
Green pepper, pea pod
Green pepper, onions
Green pepper, broccoli
Pea pods, onion
Pea pods, broccoli
Onions, broccoli

35. Making an Organized List
List all two digit numbers that can be formed using two different digits from 1, 4, 7, and 9.
Are you finding an combination or a permutation?
Each outcome is a permutation because the order of the digits matters.

36. Organized List
List all two digit numbers that can be formed using two different digits from 1, 4, 7, and 9.
Start with 1

37. Organized List
List all two digit numbers that can be formed using two different digits from 1, 4, 7, and 9.
Start with 1 14

38. Organized List
List all two digit numbers that can be formed using two different digits from 1, 4, 7, and 9.
Start with 1 14 17

39. Organized List
List all two digit numbers that can be formed using two different digits from 1, 4, 7, and 9.
Start with 1 14 17 19

40. Organized List
List all two digit numbers that can be formed using two different digits from 1, 4, 7, and 9.
Start with 1 14 17 19
Start with 4

41. Organized List
List all two digit numbers that can be formed using two different digits from 1, 4, 7, and 9.
Start with 1 14 17 19
Start with 4 41

42. Organized List
List all two digit numbers that can be formed using two different digits from 1, 4, 7, and 9.
Start with 1 14 17 19
Start with 4 41 47

43. Organized List
List all two digit numbers that can be formed using two different digits from 1, 4, 7, and 9.
Start with 1 14 17 19
Start with 4 41 47 49

44. Organized List
List all two digit numbers that can be formed using two different digits from 1, 4, 7, and 9.
Start with 1 14 17 19
Start with 4 41 47 49
Start with 7

45. Organized List
List all two digit numbers that can be formed using two different digits from 1, 4, 7, and 9.
Start with 1 14 17 19
Start with 4 41 47 49
Start with 7 71

46. Organized List
List all two digit numbers that can be formed using two different digits from 1, 4, 7, and 9.
Start with 1 14 17 19
Start with 4 41 47 49
Start with 7 71 74

47. Organized List
List all two digit numbers that can be formed using two different digits from 1, 4, 7, and 9.
Start with 1 14 17 19
Start with 4 41 47 49
Start with 7 71 74 79

48. Organized List
List all two digit numbers that can be formed using two different digits from 1, 4, 7, and 9.
Start with 1 14 17 19
Start with 4 41 47 49
Start with 7 71 74 79
Start with 9

49. Organized List
List all two digit numbers that can be formed using two different digits from 1, 4, 7, and 9.
Start with 1 14 17 19
Start with 4 41 47 49
Start with 7 71 74 79
Start with 9 91

50. Organized List
List all two digit numbers that can be formed using two different digits from 1, 4, 7, and 9.
Start with 1 14 17 19
Start with 4 41 47 49
Start with 7 71 74 79
Start with 9 91 94

51. Organized List
List all two digit numbers that can be formed using two different digits from 1, 4, 7, and 9.
Start with 1 14 17 19
Start with 4 41 47 49
Start with 7 71 74 79
Start with 9 91 94 97

52. Your Turn
You are placing a math book, a novel, and a dictionary on a shelf. List all possible ways you can order the books on the shelf.
Math book, novel, dictionary
Math book, dictionary, novel
Novel, math book, dictionary
Novel, dictionary, math book
Dictionary, math book, novel
Dictionary, novel, math book

53. I can… Self Assessment Use tree diagrams to find outcomes
Use tables or lists to find outcomes
Self Assessment
5- I can do it without help & teach others.
4- I can do this with no help, but I don’t know if I can explain it.
3- I can do this with a little help.
2- I can do this with a lot of help!
1- I don’t have a clue.

54. Finding Outcomes 13.2 Notes Methods Tree Diagram Table Organized List
Combinations – Order is NOT important
Permutations– Order is important
Methods
Tree Diagram
Table
Organized List