1. pencil, highlighter, GP notebook, textbook, calculator
U11D6
Have out:
Bellwork:
Evaluate the following WITHOUT using a calculator. (i.e. do them by hand until the last step!) +1 a)
11P6 +1 b)
11C6 +1 +1
= 332,640 +2
total:
= 462 +2

2. 1. DO NOT SOLVE! Just determine whether you would use a permutation or a combination for each of the following
a) Nathan has a dozen eggs. He wants to decorate 4 eggs for an art project.
combination
b) Mr. Gunther is lining up 12 kindergarten students for a performance.
permutation
c) Rachel has 10 valuable baseball cards. She wants to select 2 of them to sell online.
combination
d) Don has 5 soccer trophies to line up on the mantel of his fireplace.
permutation
e) Bree has to select 5 photos from a box containing 25 photos to use in the yearbook.
combination

3. Permutations and Combinations Practice
2. Solve each problem.
How many ways can Fred order a Coldstone sundae with his favorite flavor of ice cream if he chooses 4 of the 13 available toppings?
Order does not matter...
13C4 =
715
Combination
b) Joe is putting together a box of 6 pieces of See’s Candy. How many boxes are possible if there are 24 pieces Joe likes, and he gets no repeats?
Order does not matter...
Combination
24C6 =
134,596

4. c) A reading list for a course in world literature has 25 books on it
c) A reading list for a course in world literature has 25 books on it. In how many ways can you choose 3 books to read?
Order does not matter...
Combination
25C3 =
2300
d) How many different committees of 12 students can be chosen for 3 seats in ASB?
Order does not matter...
Combination
12C3 =
220

5. e) Eight sorority sisters are running for the advisory council.
In how many ways can 4 girls be chosen?
Order does not matter...
Combination
8C4 = 70
In how many ways can a president, vice–president, treasurer, and secretary be selected from the 8 girls?
Order DOES matter...
no repeats…
Permutation
8P4 =
1680

6. f) In how many ways can the B column of a Bingo card be arranged with 5 of the numbers from 1 – 15?
Order DOES matter...
no repeats…
Permutation
15P5 =
360,360
g) Five friends are assigned the 5 middle seats on a How many ways can they be arranged?
Order DOES matter...
no repeats…
Permutation 5 • 4 • 3 • 2 • 1 =
5! =
5P5 =
120

7. How many three–number “combinations” are possible if: permutations
IC – 68
Is a combination lock correctly named? Andrea bought a standard dial lock. The numbers are from 0 to 39. A combination is any three numbers… but _____ matters. Therefore, it is a ___________ lock.
order
permutation
How many three–number “combinations” are possible if:
permutations
a) no number is repeated?
40P3

8. How many three–number “combinations” are possible if:
b) repeats are allowed? 40 40 40
= 403
= 64000
Does order matter? NO
YES
Are repeats allowed?
Are repeats allowed? NO
YES NO
YES
Combination
Permutation
Decision Chart
nCr nr
nPr

9. Joaquin is getting a new locker at school and the first thing he must do is decide on a new combination. The three number combination can be picked from the numbers 0 – 21. How many different locker combinations can Joaquin choose if:
a) no number is repeated?
b) repeats are allowed?
order matters, no repeats
order matters, repeats allowed
Permutation
Decision chart/Exponent
22P3
223
= 10648

10. Can the respondents be re-interviewed (repeated)? ____
IC – 69
Replacement
a) A pollster has the names of 8 people available to answer her questions. She must select 3 of the people to interview.
When she selects interviewees, does the order of respondents matter? ______ no no
Can the respondents be re-interviewed (repeated)? ____
How many ways can she select the respondents?
Use Combination

11. b) The track team has 6 runners in a race
b) The track team has 6 runners in a race. The coach selects 2 runners to run in the first heat. In how many ways can the runners be selected?
Does order matter? no
Can the choices be repeated? no
Use Combination

12. IC – 70
Replacement
At Pete’s Perfect Pizza, all pizzas come with sauce and cheese. There are 12 toppings available (onions, pepperoni, anchovies, sausage, peppers, etc).
How many different two topping pizzas are available (with no repeated toppings)? (First decide: is this a permutation or combination???)
Use Combination
b) How many three topping pizzas are available (with no repeated toppings)?
Use Combination

13. Clear your desk except for a pencil, highlighter, and a calculator!
Quiz Time
Clear your desk except for a pencil, highlighter, and a calculator!
After the quiz, work on the rest of the assignment.

14. order matters; no repeats 8P8 = 8! = 40320
IC – 71
At Burger King®, you can “have it your way” by ordering your burger with or without mustard, ketchup, mayonnaise, lettuce, tomato, pickles, cheese, and onion.
How many ways can you “have it your way”?
8 toppings,
two choices each 2 2 2 2 2 2 2 2
= 28
explanation
= 256
b) How many ways can the condiments be arranged if you decided to order everything on your burger?
order matters; no repeats
8P8
= 8!
= 40320

15. order matters, no repeats
IC – 71
At Burger King®, you can “have it your way” by ordering your burger with or without mustard, ketchup, mayonnaise, lettuce, tomato, pickles, cheese, and onion.
c) How many combinations of any three condiments can you order on your burger?
order doesn’t matter,
no repetition
8C3
d) Suppose you only want cheese, ketchup and mustard. How many different ways can these condiments be placed on your burger?
order matters, no repeats
3P3
= 3!
= 6

16. Answer the following regarding a 10-question true/false quiz.
IC – 72
Replacement
Answer the following regarding a 10-question true/false quiz.
a) How many true/false arrangements are possible?
10 questions, two choices
210
= 1024 2 2 2 2 2 2 2 2 2 2
b) What is the probability of guessing all questions correctly?
one way to do that 1
P (all correct) =
1024
out of 1024 ways to answer

17. Answer the following regarding a 10-question true/false quiz.
IC – 72
Replacement
Answer the following regarding a 10-question true/false quiz.
c) What is the probability that none of your guesses are correct?
one way to do that 1
P (all wrong) =
1024
out of 1024 ways to answer
d) If you guess on all the questions, how many would you expect to guess correct? 1 2
P(one right) =
E(test) =
= 5 questions

18. What is the probability of guessing all questions correctly?
IC – 73
Replacement
Answer the following regarding an 8-question multiple choice quiz, with choices A, B, C, and D.
What is the probability of guessing all questions correctly?
P(right) =
P(wrong) =
b) How many arrangements of correct answers are possible? 48
= 65536 4 4 4 4 4 4 4 4
c) What is the probability of guessing all questions correctly?
P(all right) =

19. d) What is the probability of guessing none correct?
IC – 73
Replacement
Answer the following regarding an 8-question multiple choice quiz, with choices A, B, C, and D.
d) What is the probability of guessing none correct?
P (none right) =
e) What is the probability of guessing at least one question correctly?
P (at least 1 correct) =
1 – P (none correct)
f) If you guess on all the questions, how many would you expect to guess correct?
E(Test) =
correct
P(right) =

20. Finish the assignment:
IC 77, 78, 80, 81, and worksheet

21. just for “fun” activity
Optional
just for “fun” activity

22. It’s quiz time! T F F F F T T F F T
Flip to the back of today’s worksheets:
FOR FUN: Let’s go back to the quizzes in IC – 72 and IC – 73.
It’s quiz time!
IC – 72: Choose either TRUE or FALSE for questions 1 – 10. Fill in your answers below, then make a histogram of the data from the class.
It’s time to grade the quiz!!! Take out a red pen.
The answers are… T F F F F T T F F T
1. __
2. __
3. __
4. __
5. __
6. __
7. __
8. __
9. __
10. __
Write the number correct out of 10 on your worksheet.

23. Let’s make a bar graph of the results of our class.7 6 5
# of students 4 3 2 1 1 2 3 4 5 6 7 8 9 10
# of correct answers.
How does the class data compare to the expected value?

24. IC – 73: Choose A, B, C, or D for questions 1 – 8
IC – 73: Choose A, B, C, or D for questions 1 – 8. Fill in your answers below, then make a histogram of the data from the class.
It’s time to grade the quiz!!! Take out a red pen.
The answers are… C D C D A C A A
1. __
2. __
3. __
4. __
5. __
6. __
7. __
8. __
Write the number correct out of 8 on your bellwork.

25. Let’s make a bar graph of the results of our class.7 6 5
# of students 4 3 2 1 1 2 3 4 5 6 7 8
# of correct answers.
How does the class data compare to the expected value?

26. Would you like mustard, ketchup, mayonnaise, lettuce, tomato, pickles, cheese, and onion?2
yes no
ketchup x2
yes no
yes no x2
mayonnaise . . .
yes no
and on and on…
28 = 256
Return

27. old bellwork

28. pencil, highlighter, GP notebook, textbook, calculator
3/26/10
Have out:
Bellwork:
a) On the way to the movies you and your 7 friends get ice cream. The place you are going simply mixes up the ingredients before serving them in a cup. How many different kinds of different ice cream cups can you have if you can only get 3 scoops and there are 12 different flavors (no repetition allowed)?
b) 8 people go to the movies. The people include a pair of conjoined twins, one of their dates, two other friends with both of their dates, and you are a loner. (So sad , but you are not the only one! The other conjoined twin is a loner too… sort of.) How many different ways are there to arrange yourselves?

29. a) On the way to the movies you and your 7 friends get ice cream
a) On the way to the movies you and your 7 friends get ice cream. The place you are going simply mixes up the ingredients before serving them in a cup. How many different kinds of different ice cream cups can you have if you can only get 3 scoops and there are 12 different flavors (no repetition allowed)?
Does order matter? NO
YES
Can I repeat myself?
Can I repeat myself? NO
YES NO
YES
Combination
Permutation
Decision Chart
nCr nr
nPr

30. another way if you forgot this...
a) On the way to the movies you and your 7 friends get ice cream. The place you are going simply mixes up the ingredients before serving them in a cup. How many different kinds of different ice cream cups can you have if you can only get 3 scoops and there are 12 different flavors (no repetition allowed)?
12C3
same thing
another way if you forgot this... 12 11 10
order doesn’t matter, so divide by the arrangements 3!

31. b) 8 people go to the movies
b) 8 people go to the movies. The people include a pair of conjoined twins, one of their dates, two other friends with both of their dates, and you are a loner. (So sad , but you are not the only one! The other conjoined twin is a loner too… sort of.) How many different ways are there to arrange yourselves?  
How many groups are we arranging?
4 groups
Only two groups can change up internally. 4! 2! 2!
= 96