1. pencil, highlighter, GP notebook, textbook, calculator
U11D3
Have out:
Bellwork:
Start IC – 34 on the worksheet.
IC – 34
To choose a PIN (__________ _____________ ________)
at a certain bank, you select 4 numbers from the digits 0 – 9,
with no repeats. How many are possible? Make a decision
chart to help you determine the answer.
personal
identification
number
total:

2. Factorials to Permutations
IC – 34
Factorials to Permutations
To choose a PIN (__________ _____________ ________)
at a certain bank, you select 4 numbers from the digits 0 – 9,
with no repeats. How many are possible? Make a decision
chart to help you determine the answer.
personal
identification
number +2 +2 10 9 8 7
_____ _____ _____ _____ =
5040 7
This looks like the beginning of 10!, but only down to _____,
so the _____ is divided out.
_____ _____ _____ _____ = 6! 10 9 8 7
So there are 4 spots to fill and 10 options to start with. How can I get a 6 out of this?
10 – 4 = 6
total:

3. You’ve won 14 trophies since grade school. Your mom says that
IC – 35
You’ve won 14 trophies since grade school. Your mom says that
only 3 trophies can go on the mantle. In how many ways can you
choose and arrange them? 14 13 12
2184
_____ _____ _____ = 12
This looks like the beginning of 14!, but only down to _____
with _____ divided out.
_____ _____ _____ =
11! 14 13 12
So there are 3 spots to fill and 14 options to start with. How can I get an 11 out of this?
14 – 3 = 11

4. Fifty–two women vie for the “Miss USA” crown. In how many
IC – 36
Solve the following problems. Use factorials to express each of the following solutions.
Fifty–two women vie for the “Miss USA” crown. In how many
ways can a winner and her three runner–ups be chosen? 52 51 50 49
_____ _____ _____ _____ =
6,497,400
How can I write this as factorials?
52 – 4 = 48

5. Try b and c in your groups!
b) The ECHS volleyball team is sponsoring a mixed–doubles
sand court volleyball tournament and sixteen pairs have signed
up for the chance to win one of the seven trophies and cash
prizes. In how many ways can the teams be chosen and
arranged for the top seven slots?
Carmen is getting a new locker at school and the first thing she
must do is decide on a new combination. The three number
combination can be picked from the numbers 0 – 35. How
many different locker combinations could she make up if none
of the numbers can be repeated?

6. b) The ECHS volleyball team is sponsoring a mixed–doubles
IC – 36
b) The ECHS volleyball team is sponsoring a mixed–doubles
sand court volleyball tournament and sixteen pairs have signed
up for the chance to win one of the seven trophies and cash
prizes. In how many ways can the teams be chosen and
arranged for the top seven slots?
Remember, each pair is one entity. 16 15 14 13 12 11 10
_____ _____ _____ _____ _____ _____ _____ =
57,657,600
How can I write this as factorials?
16 – 7 = 9

7. Carmen is getting a new locker at school and the first thing she
IC – 36
Carmen is getting a new locker at school and the first thing she
must do is decide on a new combination. The three number
combination can be picked from the numbers 0 – 35. How
many different locker combinations could she make up if none
of the numbers can be repeated? 36 35 34
42,840
_____ _____ _____=
36?! But it only went to 35!
Oh, 0 – 35 is 36 different numbers.
How can I write this as factorials?
36 – 3 = 33

8. PERMUTATIONS Per around perimeter periscope
“_______” means ________, as in __________ or _________.
Mutation
change
“__________” means __________.
Problems where we are concerned about order and
arrangements are called ________________.
permutations
For example, the 6 arrangements of the letters ABC are
permutations.
Purrrrrr!
ABC
CBA
ACB
CAB
BCA
BAC
The two main characteristics of a permutation are
_____ ____________ and __________ matters. NO
REPETITION
ORDER

9. There are two important questions we must ask from here on out.
1) Does order matter?
2) Are repeats allowed?
Here is a flowchart to help you out. We will fill in the rest when
we talk about combinations.
Does order matter? NO
YES
Are repeats allowed?
Are repeats allowed? NO
YES NO
YES
__________
(Leave blank)
Combination
Permutation
Decision Chart

10. Practice: Determine whether or not the given situations are
permutations or not.
a) All the arrangements of the letters ABC.
All the possible license plate letter triples that could be made using A, B, C.
c) The possible 4–digit numbers you could make if you had square tiles, one with each number 2, 3, 4, 5, 6, 7, 8
The possible 4–digit numbers you could make if you could choose any digit from 2, 3, 4, 5, 6, 7, 8
e) From a group of 8 candidates, one will become president, one vice president, and one secretary of the school senate.
f) From a group of 8 candidates, three will be selected to be on the executive committee.

11. Practice: Determine whether or not the given situations are
permutations or not.
a) All the arrangements of the letters ABC.
All the possible license plate letter triples that could be made using A, B, C.
Permutation
Not a permutation
Does order matter? NO
YES
Are repeats allowed?
Are repeats allowed? NO
YES NO
YES
Combination
Permutation
Decision Chart

12. Try c, d, e, and f in your groups!
Does order matter? NO
YES
Are repeats allowed?
Are repeats allowed? NO
YES NO
YES
Combination
Permutation
Decision Chart

13. Practice: Determine whether or not the given situations are
permutations or not.
c) The possible 4–digit numbers you could make if you had square tiles, one with each number 2, 3, 4, 5, 6, 7, 8
The possible 4–digit numbers you could make if you could choose any digit from 2, 3, 4, 5, 6, 7, 8
Permutation
Not a permutation
Does order matter? NO
YES
Are repeats allowed?
Are repeats allowed? NO
YES NO
YES
Combination
Permutation
Decision Chart

14. Practice: Determine whether or not the given situations are
permutations or not.
e) From a group of 8 candidates, one will become president, one vice president, and one secretary of the school senate.
f) From a group of 8 candidates, three will be selected to be on the executive committee.
Not a permutation
Permutation
Does order matter? NO
YES
Are repeats allowed?
Are repeats allowed? NO
YES NO
YES
Combination
Permutation
Decision Chart

15. nPr PERMUTATION NOTATION selecting arranging
nPr is the notation for _________ and _________ r things from n things.
Add nPr to the flowchart.
Does order matter? NO
YES
Are repeats allowed?
Are repeats allowed? NO
YES NO
YES
___________
(Leave blank)
Combination
Permutation
Decision Chart
nPr

16. things you are choosing from n = # of ______________________________
IC – 38
Eight people are running a race. In how many different ways can they come in first, second, and third?
things you are choosing from
n = # of ______________________________
r = # of ______________________________
things you are choosing 8
For this problem, n = ____ and r = ____ 3
_____ =

17. Try parts (b) and (c) on your own.
Flip your worksheet over. Let’s go back and solve IC 34 – 36 using permutations this time.
IC – 34
To choose a PIN at a certain bank, you select 4 numbers from the digits 0 – 9, with no repeats. How many are possible?
We going to select and arrange 4 numbers from a group of 10 possible numbers.
10P4 =
= 5040
IC – 36
Fifty–two women vie for the “Miss USA” crown. In how many
ways can a winner and her three runner–ups be chosen?
We going to select and arrange 4 women from a group of 52 women.
52P4 =
= 6,497,400
Try parts (b) and (c) on your own.

18. b) The ECHS volleyball team is sponsoring a mixed–doubles
IC – 36
b) The ECHS volleyball team is sponsoring a mixed–doubles
sand court volleyball tournament and sixteen pairs have signed
up for the chance to win one of the seven trophies and cash
prizes. In how many ways can the teams be chosen and
arranged for the top seven slots?
We going to select and arrange 7 teams from a group of 16 possible teams.
16P7 =
= 57,657,600
The three number combination can be picked from the numbers 0 – 35. How many different locker combinations could be made up if none of the numbers can be repeated?
We going to select and arrange 3 numbers from a group of 36 possible numbers.
36P3 =
= 42,840

19. Ice Cream Shop
Try the Ice Cream problem in your groups!

20. You go to 31 flavors Ice Cream. Determine the number of
ways you can order the following on an ice cream cone.
a single scoop
a double scoop (with repeats allowed) 31 31 31
= 961
Does order matter? NO
YES
Are repeats allowed?
Are repeats allowed? NO
YES NO
YES
Combination
Permutation
Decision Chart
nPr

21. You go to 31 flavors Ice Cream. Determine the number of
ways you can order the following on an ice cream cone.
c) a double scoop (with no repeats)
a triple scoop (with repeats
allowed) 31 31 31
= 29,791
Does order matter? NO
YES
Are repeats allowed?
Are repeats allowed? NO
YES NO
YES
Combination
Permutation
Decision Chart
nPr

22. You go to 31 flavors Ice Cream. Determine the number of
ways you can order the following on an ice cream cone..
a triple scoop (with no repeats)
Does order matter? NO
YES
Are repeats allowed?
Are repeats allowed? NO
YES NO
YES
Combination
Permutation
Decision Chart
nPr

23. Finish the assignment:
Log Practice and IC 40, 41, 43 – 48