# pencil, highlighter, GP notebook, textbook, calculator Evaluate the

pencil, highlighter, GP notebook, textbook, calculator Evaluate the following WITHOUT using a calculator. (i.e. do them by hand until the last step!) 11! 11! +1 P C +1 a) 11 6 b) 11 6 (11 6)!6! (11 6)! 11! 11! 5!6! 5! 11 10 9 8 7 6!

11 10 9 8 7 6 5! +1 +1 5!6! 5! 11 10 9 8 7 = 332,640 +2 120 +2 = 462 total: 8 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 2. Solve each problem. a) 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... 13 C4 = 715 Combination

b) Joe is putting together a box of 6 pieces of Sees Candy. How many boxes are possible if there are 24 pieces Joe likes, and he gets no repeats? Order does not matter... Combination 24 C6 = 134,596 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 25 C3 = 2300 d) How many different committees of 12 students can be chosen for 3 seats in ASB? Order does not matter... Combination 12 C3 = 220 e) Eight sorority sisters are running for the advisory council.

In how many ways can 4 girls be chosen? Order does not matter... Combination 8 C4 = 70 In how many ways can a president, vicepresident, treasurer, and secretary be selected from the 8 girls? Order DOES matter... 8 P4 = 1680 no repeats Permutation 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 15 P5 = 360,360 g) Five friends are assigned the 5 middle seats on a 747. How many ways can they be arranged? Order DOES matter... no repeats Permutation 5 4 3 2 1

= 5! = 5P5 = 120 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 order matters. Therefore, it is a ___________ permutation lock. _____ permutations are possible if: How many threenumber combinations a) no number is repeated? 40! 40! P 40 39 38 59,280 40 3 (40 3)! 37!

How many threenumber combinations are possible if: b) repeats are allowed? 40 40 40 = 403 = 64000 Does order matter? NO Are repeats allowed? NO Combination nCr YES

YES Are repeats allowed? NO Permutation n Pr YES Decision Chart nr 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? order matters, no repeats Permutation 22P3 22! 22 P3 (22 3)! 22!

19! 22 2120 9240 b) repeats are allowed? order matters, repeats allowed Decision chart/Exponent 223 = 10648 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 no respondents matter? ______

no Can the respondents be re-interviewed (repeated)? ____ How many ways can she select the respondents? Use Combination 8! 8 7 6 8! 4 7 2 56 8 C3 (8 3)!3! 5!3! 3 2 1 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 6 C2

6! 6! 6 5 3 5 15 (6 2)!2! 4!2! 2 1 IC 70 Replacement At Petes Perfect Pizza, all pizzas come with sauce and cheese. There are 12 toppings available (onions, pepperoni, anchovies, sausage, peppers, etc). a) How many different two topping pizzas are available (with no repeated toppings)? (First decide: is this a permutation or combination???) Use Combination 12! 12 11

12! 6 11 66 12 C 2 2 1 (12 2)!2! 10!2! b) How many three topping pizzas are available (with no repeated toppings)? Use Combination 12! 12 1110 12 2 1110 220 12 C 3 3 2 1 (12 3)!3! 9!3! Clear your desk except for a pencil, highlighter, and a calculator! After the quiz, work on the rest of the assignment.

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. a) How many ways can you have it your way? 8 toppings, two choices each 2 2 2 2 2 2 2 2 = 28 = 256 explanation b) How many ways can the condiments be arranged if you decided to order everything on your burger?

order matters; no repeats 8 P8 = 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. c) How many combinations of any three condiments can you order on your burger? order doesnt matter, no repetition 8! 8! 8 7 6 56 8C3

(8 3)!3! 5!3! 3 2 1 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 3 P3 = 3! = 6 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 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? 1 one way to do that 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 P(one right) = 2 E(test) = 1 (10) = 5 questions 2 IC 73 Replacement Answer the following regarding an 8-question multiple choice quiz, with choices A, B, C, and D. a) What is the probability of guessing all questions correctly? 1 P(right) = 4

3 P(wrong) = 4 ) 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? 1 P(all right) = 65536 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?

8 3 6561 0.10 P (none right) = 4 65536 e) What is the probability of guessing at least one question correctly? P (at least 1 correct) = 1 P (none correct) 1 0.10 0.90 f) If you guess on all the questions, how many would you expect to guess correct? 1 (8) 2 correct E(Test) = 1 4

P(right) = 4 Finish the assignment: IC 77, 78, 80, 81, and worksheet Optional just for fun activity Flip to the back of todays worksheets: FOR FUN: Lets go back to the quizzes in IC 72 and IC 73. 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. Its time to grade the quiz!!! Take out a red pen. The answers are T 2. __ F 3. __ F 4. __ F 5. __

F 6. __ T 7. __ T 8. __ F 9. __ F 10. __ T 1. __ Write the number correct out of 10 on your worksheet. Lets make a bar graph of the results of our class. 7 6 # of students 5 4 3 2 1 1 2

6 7 3 4 5 # of correct answers. 8 9 How does the class data compare to the expected value? 10 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. Its time to grade the quiz!!! Take out a red pen. The answers are C 2. __ D 3. __ C 4. __

D 5. __ A 6. __ C 7. __ A 8. __ A 1. __ Write the number correct out of 8 on your bellwork. Lets make a bar graph of the results of our class. 7 6 # of students 5 4 3 2 1 1 2

6 7 3 4 5 # of correct answers. 8 How does the class data compare to the expected value? Would you like mustard, ketchup, mayonnaise, lettuce, tomato, pickles, cheese, and onion? mustard 2 yes no ketchup x2

yes no yes no x2 mayonnaise . . . Return yes no . . .

. and on and on . 28 = 256 . old bellwork pencil, highlighter, GP notebook, textbook, calculator 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?

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 Can I repeat myself? NO Combination nCr YES YES Can I repeat myself? NO Permutation n Pr YES

Decision Chart nr 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)? n! n Cr (n r)! r! C3 12 12! 12! 12 1110

4 115 220 12 C 3 3 2 1 (12 3)!3! 9!3! same thing 12 11 3! 10 order doesnt matter, so divide by the arrangements 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

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