Statistics and Probability Name ______________________4.1 The Fundamental Counting Principle ASSIGNMENT Hour ______ Date ___________

1. Margaret is the keynote speaker at tomorrow’s Board of Directors meeting. She can select any one of eight skirts, five blouses, four blazers, and six pairs of shoes to wear to the meeting. If an outfit consists of a skirt, blouse, blazer, and pair of shoes, how many different outfits are possible?

2. How many different ways can the letters in the word CANDY be arranged?

3. The 28-choices ice cream shop offers 28 flavors of ice cream, 11 different toppings, and 3 sizes of bowl for their ice cream sundaes. In how many ways can you order a sundae with one scoop of ice cream and one topping?

4. A postal employee is scheduling this morning’s seven special deliveries. How many different schedules are possible?

5. How many different outfields can a coach have if he has five left fielders, four center fielders, and five right fielders? (An outfield consists of one left fielder, one center fielder, and one right fielder).

6. Look at the menu below.Entrees Sides Desserts

Chicken Rice Lemon PieBeef Baked Potato CheesecakeFish Steamed Vegetables PuddingTofu Stuffing

a. How many different orders can you make consisting of one entrée and one side?

b. How many different orders can you make consisting of one entrée and two sides? (Assume youcannot pick the same side twice).

c. How many different orders can you make consisting of one entrée, one side, and one dessert?

7. You are given the instructions to write down a 3 digit number. You can only use the digits 1 through 9.

a. If you are allowed to use a digit more than once, determine the number of 3 digits numbers that can be made.

b. If you are not allowed to use a digit more than once, determine the number of 3 digits numbers that can be made.

8. Suppose you run a business, and you need to issue passwords to your customers, so they can access an online system. Your passwords will have the form of two upper case letters (chosen from the 26 letter alphabet) followed by three digits (chosen from 0, 1, …, 9). Here’s one example of a possible password: BZ122. Letter and digit choices may be repeated.

a. Determine how many different passwords can be made using this format.

b. If your company has more than 1 million customers, will you have enough passwords using the format above? If not, suggest a change in the format of the passwords that would generate enough possibilities to cover 1 million or more customers. How many different passwords can be generated using your new suggested format?

9. Suppose there are 23 people in attendance at a meeting. There are four door prizes to give away. The 23 people will put their names in a hat (one slip of paper per person). The names will be drawn out of the hat to award the prizes.

a. If it is possible for the same person to be awarded more than one prize, in how many different ways can the door prizes be awarded?

b. The situation above is not typical. The typical situation is one in which a person’s name is removed from the hat and not replaced once he/she has won a prize. How many different ways are there to award the four door prizes in this setting?

c. Which of the above questions (a or b) is an example of selection without replacement?

Statistics and Probability Name ______________________4.2 Specific Positions ASSIGNMENT Hour ______ Date ___________

1. Five students (Caleb (B), Jordan (B), Gustavo (B), Dezarae (G), and Anna (G)) are going to sit in a row at a movie theater. (B: boy, G: girl).

a. How many ways can they be seated?

b. How many ways can they be seated if Jordan must be in the fourth seat?

c. How many ways can they be seated if a boy must be on each end?

d. How many ways can they be seated if Anna must be first and a boy must be in the 3rd seat?

e. How many ways can they be seated if the girls must sit in the first two seats?

2. How many 5 letter words can Francisco form from all the letters in the alphabet, if repetitions are allowed and each arrangement of letters does not necessarily have to form a meaningful word?

3. How many four-letter words can Laura create from the letters in the word DIPLOMA if the word must begin with L and letters can be repeated?

4. A coat hanger has four knobs. If Matt has 6 different colors of paint available (and colors may be repeated), in how many ways can he paint the knobs?

5. Brandon is giving a presentation at a business meeting. He needs to select an outfit consisting of a shirt, tie, and pair of pants. If he has six shirts, eight ties, and three pairs of pants from which to choose, how many outfits are possible?

6. There are 10 buildings on a college campus. In how many orders can Joel visit all of them?

7. In how many ways can Alyson put five lions and four tigers alternately in a row of nine cages?

8. Ashly has been put in charge of forming a committee consisting of a president, a vice-president, and a treasurer. There are 10 people from which to be selected. How many committees are possible if a person can only hold one position?

9. How many numbers less than 700 of three different digits each can be formed from the digits 1, 2, 3, 4, 5, 6, 7, 8, and 9?

10. How many four-digit even numbers can be formed from the digits 5, 7, 8, and 9 if digits can be repeated?

11. How many four-digit even numbers can be formed from the digits 5, 7, 8, and 9 if digits cannot be repeated?

12. If there are 5 light switches on an electrical panel, how many orders of on/off are there?

Statistics and Probability Name ______________________4.3 Permutations and Combinations ASSIGNMENT Hour ______ Date ___________

1. In how many ways may a committee of 6 be chosen from a group of 25 people?

permutation / combination

2. A group of fifteen men wish to play on a basketball team. Find the number of teams that can be formed if there are 5 men chosen for a team.

permutation / combination

3. In how many ways can a judge award first, second, and third places in a contest with fourteen entrees if there are not ties?

permutation / combination

4. A track coach has a group of seven men to choose from in order to have a four-man relay team. How many line-ups can he form (order matters)?

permutation / combination

5. How many ways can a president, vice-president, and secretary be chosen from a committee of 7 people?

permutation / combination

6. A bicycle owner has 12 mountain bikes in the showroom. The owner wishes to display 4 of them at a bicycle show. How many different ways can 4 bikes be arranged in a line to be displayed?

permutation / combination

7. How many different 5-card hands can be formed from a standard deck of cards?

permutation / combination

For #1-7, a. Determine whether the situation involves a combination or a permutation. b. Solve the problem.

Review:8. How many 4-letter words can be made from the first 6 letters of the alphabet if repetitions are not

allowed and each arrangement of letters does not necessarily have to form a meaningful word?

9. How many different license plates are possible if each contains 2 letters followed by 3 digits (0, 1, …, 9) and digits and letters may be repeated?

10. Joey and Julie are lined up with 10 family members (12 people total) for a photo at a family gathering.

a. In how many ways can all 12 family members be arranged?

b. In how many ways can all 12 family members be arranged if Joey must be positioned at the far left end of the line, and Julie must be at the far right end of the line?

11. Tonya is taking a geology quiz. How many ways can she answer all the questions on the quiz if

a. the quiz has 7 true-false questions?

b. the quiz has 7 multiple-choice questions, each having 4 answer choices?

12. How many 4-digit numbers (for a number to be a 4-digit number, it cannot start with 0) exist

a. that are odd?

b. that are odd and larger than 4000?

c. that have only odd digits?

d. that have only even digits?

Statistics and Probability Name ______________________4.4 Permutations and Combinations for Multiple Groups Hour ______ Date ___________

ASSIGNMENT

1. How many two-letter, three-letter, or four-letter words can be formed from the word PENCIL if the letters cannot be repeated? The letters do not necessarily need to form meaningful words.

2. How many numbers of at most three different digits can be formed from the number 1, 2, 3, 4, and 5 if digits cannot be repeated?

3. How many odd numbers of at most four different digits can be formed from the numbers 1, 2, 3, 4, 5, 6 if the digits cannot be repeated?

4. There are 8 parents and 43 students going on a school trip. Two groups are made, a large one with 30 students and 5 parents, and a small group with 13 students and 3 parents.

a. How many different ways can the parents be chosen for the small group?

b. How many ways can the students be chosen for the large group if Steven and Dylan must be in the small group?

c. How many ways can students be chosen for the small group if Will and both his parents must be in the small group?

Review:

5. Each year, readers of a certain magazine are asked to rank the top 5 best-dressed men from among a list of 17 candidates. In how many different ways can this be done?

6. How many different 11-member football teams can be formed from a possible 20 players?

7. The ten-member Board of Directors of a company wishes to elect a chairperson, a secretary, an executive officer, and a comptroller from among the ten members. In how many different ways can this be done? Assume that a person can hold only one position.

8. A baseball manager has selected his nine starting players. How many different batting orders are possible?

9. Stephanie Wilson is planning a trip to see her aunt and uncle who live in Washington, D.C. There are ten different places of interest that Stephanie wishes to visit; however, Stephanie’s schedule will permit her the time to see only six of them.

a. If the order of the visits matters, in how many ways can Stephanie plan her trip?

b. If the order of the visits does not matter, in how many ways can Stephanie plan her trip?

10. How many different ways are there to answer an 8-question multiple-choice quiz where each question has five answer choices?

11. How many different computer passwords can be created if each is to consist of five letters followed by three numbers and if

a. repetition of numbers and letters is allowed?

b. repetition of numbers and letters is not allowed?

c. only letters cannot be repeated?

Statistics and Probability Name ______________________4.5 Letter Repetitions, Items Always Together, Hour _____ Date ____________Handshakes, Selections Pools ASSIGNMENT

1. How many ways can the letters in the word VACATION be arranged?

2. How many ways can the letters in the word HIPPOPOTAMUS be arranged?

3. How many ways can the letters in the word SUNBURN be arranged?

4. How many ways can the letters in OBTUSE be arranged if all the vowels must be kept together?

5. How many ways can the letters in the word KEYBOARD be arranged if A and Y must be kept together?

6. How many ways can 4 rock, 5 pop, 6 country, and 3 jazz CD’s be arranged on a shelf if all the CD’s of the same type must be kept together?

7. In a train yard there are 4 tank cars, 12 boxcars, and 7 flatcars. How many ways can a train be made up consisting of 2 tank cars, 5 boxcars, and 3 flatcars? Assume that the order of the cars is not important.

8. There are 8 women and 6 men in a department.

a. How many ways can a committee of 5 people be selected?

b. How many ways can this committee be selected if there must be 3 women and 2 men on the committee?

9. Five cards are drawn from a standard deck of cards.

a. How many 5-card hands consist of 4 clubs and 1 spade?

b. How many 5-card hands consist of three 6’s and two queens?

10. Thirty people at a business meeting shake hands once with everyone else in the room. How many handshakes took place?

Statistics and Probability Name ______________________4.6 Binomial Probabilities ASSIGNMENT Hour _____ Date ____________

1. Ninety percent of the trees planted by a particular landscaping firm survive. What is the probability that exactly eight of the 15 trees just planted will survive?

Success =

n =

p =

q =

k =

2. In California, 30% of the people have a certain blood type. What is the probability that exactly 5 out of a randomly selected group of 14 Californians will have that blood type?

Success =

n =

p =

q =

k =

For #1-5, a. define a success.b. identify n (number of trials), p (probability of a success), q (probability of failure) and

k (number of successes). c. show the values n, p, and k correctly substituted into the binomial probability formula.

P(k successes) = nCk(p)k(q)(n – k)

d. find the designated probability.

3. One-fourth of a certain breed of rabbits are born with long hair. What is the probability that in a litter of six rabbits, exactly three will have long hair?

Success =

n =

p =

q =

k =

4. A January 2005 survey of bikers, commissioned by the Progressive Group of Insurance Companies, showed that 40% of bikers have body art, such as tattoos and piercings. A group of 10 bikers are in the process of planning a trip across the country. What is the probability that none of them have body art?

Success =

n =

p =

q =

k =

5. On average, 1 out of every 10 boards purchased by a cabinet manufacturer is unusable for building cabinets. What is the probability that 8 of a set of 11 such boards are usable?

Success =

n =

p =

q =

k =

Statistics and Probability Name ______________________4.6 Binomial Probabilities, Day 2 ASSIGNMENT Hour _____ Date ____________

1. Approximately 51% of the babies born in the US each year are girls. Suppose that 12 babies are born at Holland Hospital on December 13, 2011. What is the probability that half of the babies are girls?

Success =

n =

p =

q =

k =

2. 68% of 18- to 29-year olds who voted in the 2008 presidential election voted for Obama. Suppose a sample of 10 people who voted in the 2008 election and are between the ages of 18 to 29 is selected. What is the probability that 3 of them voted for Obama?

Success =

n =

p =

q =

k =

For #1-3, a. define a success.b. identify n (number of trials), p (probability of a success), q (probability of failure) and

k (number of successes). c. show the values n, p, and k correctly substituted into the binomial probability formula.

P(k successes) = nCk(p)k(q)(n – k)

d. find the designated probability.

3. A study by the Center for Disease Control in 2009 showed that 17.2% of high school students reported that they were “current cigarette smokers”. A sample of 30 students is taken. What is the probability that 20 of them are non-smokers?

Success =

n =

p =

q =

k =

Review:

4. A test consists of 6 multiple choice questions each with 4 answer choices and 3 true-false questions. In how many ways can a student answer all the quiz questions?

5. How many ways can the letters in the word SURFING be arranged?

6. How many ways can the letters in the word SNOWSTORM be arranged?

7. If there are 45 people at a party and everyone shakes hands with everyone else once, how many handshakes will take place?

8. How many ways can the letters in the word SEMINAR be arranged if the S and A must be together and the I, E,and R must be together?

9. In how many ways can 7 friends (Amy, Brian, Charlie, Dave, Eric, Fred, Grace) sit in a row at a movie theater if Amy and Grace have to sit together?

Statistics and Probability Name ______________________4.7 Binomial Probabilities: At Least/At Most ASSIGNMENT Hour _____ Date ____________

1. The probability that a high school student will graduate at a particular school is 0.72. Out of 8 students, determine the probability that:

a. exactly 3 students graduate.

Success =

n =

p =

q =

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b. at least 7 students graduate.

Success =

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p =

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c. at least 2 students graduate.

Success =

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2. Jason flips a fair coin 12 times and observes the number of tails. Find the probability of tossing exactly 8 or 9 tails.

Success =

n =

p =

q =

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3. Lindsey, a wildlife biologist, examines frogs for a genetic trait she suspects may be linked to sensitivity to industrial toxins in the environment. Previous research had established that this trait is usually found in 1 of every 8 frogs. Lindsey collects and examines a dozen frogs. If the frequency of the trait has not changed, what’s the probability she finds the trait in

a. none of the 12 frogs?

Success =

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q =

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b. no more than 2 frogs?

Success =

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5. Eight students: Deshaun(B), Drew(B), Scott(B), Greg(B), Jake(B), Danielle(G), Morgan (G), and

Katie(G) are going to stand in a line. (B: boy, G: girl). How many ways can they stand if

a. Drew must be in the 3rd position? Show all calculations.

b. the first two positions are boys and the last three are girls? Show all calculations.

c. a girl must be on both ends? Show all calculations.

d. Jake must be in the 6th position and a girl must be in the last position? Show all calculations.

e. Scott cannot be on either end? Show all calculations.

6. Suppose a data set has a mean of 20 and a standard deviation of 12.

a. If each value in the data set is increased by 11, what will be the new mean and standard deviation?

Mean = ________ Standard Deviation = _________b. If each value in the data set is divided by 4, what will be the new mean and standard

deviation?Mean = ________ Standard Deviation = _________

7. How many ways can the letters in the word HONESTY be arranged if the H and O must be kept together and the E, S, and T must be kept together? Show all calculations.

8. How many ways can the letters in the word TSUNAMI be arranged if the word must start with a vowel and end with M? Show all calculations.

9. How many ways can the letters in the word TENNESSEE be arranged? Show all calculations.

10. How many five-digit even numbers can be formed from the digits 2, 3, 5, 6, 7, and 8 if digits may be repeated? Show all calculations.

11. A medical clinic classifies patients’ files by gender and by type of diabetes (A or B). The number of patients in each classification is shown below.

Type of DiabetesGender A B TotalMale 50 40 90Female 35 75 110Total 85 115 200

a. If a person is selected at random, what is the probability that the selected individual is female?

b. If a person is selected at random, what is the probability that the selected individual is male or has type B diabetes? Show all calculations.

c. If a person is selected at random, what is the probability that the selected individual is female given that the individual has type A diabetes?

d. If a person is selected at random, what is the probability that the selected individual has type A diabetes given that the individual is female?

12. A school club has 10 freshmen, 16 sophomores, 19 juniors, and 15 seniors. Two students are going to be randomly selected to plan an upcoming school event. What is the probability of selecting a junior followed by a senior? Show all calculations.

Statistics and Probability Name ______________________Chapter 4 Additional Practice 1 ASSIGNMENT Hour _____ Date ____________

Permutations CombinationsWith Repetition Without Repetition Without Repetition

If there are n things to choose from, and you choose r of them, then the number of possible permutations is:

nr

If there are n things to choose from, and you choose r of them, then the number of possible permutations is:

nPr =

n!(n−r ) !

If there are n things to choose from, and you choose r of them, then the number of possible combinations is:

nCr =

n!(n−r )!r !

Binomial ProbabilityFor a binomial setting with n trials where p is the probability of success on each trial, the probability of exactly k successes is

P(k successes) = nCk(p)k(q)(n – k)

1. A research team at Cornell University conducted a study showing that approximately 10% of all businessmen who wear ties wear them so tight that they actually reduce blood flow to the brain, diminishing cerebral functions (Source: Chances: Risk and Odds in Everyday Life, by James Burke). For a board meeting of 20 businessmen, all of whom wear ties, find the following probabilities. Assume the conditions for a binomial experiment/setting have been met.

a. What is the probability that exactly 5 men are wearing ties that are too tight? Round to 3 decimal places.

Success =

n =

p =

k =

b. What is the probability that no men are wearing ties that are too tight? Round to 3 decimal places.

Success =

n =

p =

k =

2. The board of directors of Belford Community Hospital has 12 members. Four officers (president, vice-president, secretary, and treasurer) must be elected from the members. How many possible slates of officers are there if no one can hold more than one office?

3. Three members from the group of 12 on the board of directors at Belford Community Hospital will be selected to go to a convention. How many groups of 3 are possible?

4. The Deli Special lunch offers a choice of seven different sandwiches, four kinds of salads, and five different desserts. How many lunches does Joe have to select from if each lunch consists of one sandwich, one salad, and one dessert?

5. How many ways can Noah arrange 9 video game cartridges on a shelf?

6. How many ways can 8 people (Joe, Kelly, Lisa, Matt, Nicole, Owen, Peter, and Quinton) stand in a line for a photo if all the girls (Kelly, Lisa, Nicole) want to stand together?

7. Several DVD’s are being placed on a shelf. There are 5 drama movies, 8 comedy movies, and 2 action movies. How many ways are there of arranging the DVD’s if the movies of the same genre must be kept together?

8. Sixteen people at a formal gathering shake hands once with everyone else in the room. How many handshakes took place?

9. Wake-Up cereal comes in twp types, crispy and crunchy. Veronica, a researcher, has 9 boxes of the crispy cereal and 11 boxes of the crunchy cereal. In how many ways can she select 3 boxes of crispy cereal and 3 boxes of crunchy cereal for a quality control test?

10. Melanie must take one literature, one social science, and one art class this semester. There are four literature courses, three social science courses, and three art courses from which to select. In how many ways may Melanie select the courses to fulfill the requirement?

11. How many five letter words can be created from DISCOVERY if repetitions are not allowed? The letters do not necessarily need to form meaningful words.

12. How many four-digit odd numbers can be formed from the digits 1, 2, 3, 4, 6, 8, and 9 if digits cannot be repeated?

13. How many numbers of at least 5 different digits can be created from the digits 1, 2, 3, 4, 6, 8, and 9?

14. How many four digit numbers less than 3000 can be created from the digits 1, 2, 3, 4, 6, 8, and 9 if digits cannot be repeated?

15. How many passwords can be created if each password is to contain 4 letters followed by 2 numbers (0, 1, 2, …, 9) and

a. letters and numbers may be repeated?

b. letters and numbers may not be repeated?

16. Ten students: Ryan(B), Jason(B), Tyler(B), Nick(B), Mathias(B), Rachell(G), Mandy(G), Linh(G), Eliza(G), and Haleigh (G) (B: boy, G: girl). How many ways can they stand if

a. Jason must be in the 3rd position?

b. the first three positions are boys and the last two are girls?

c. a boy must be on both ends?

26. Dakota is taking a math quiz. How many ways can he answer all the questions on the quiz if

a. the quiz has 8 true-false questions?

b. the quiz has 6 multiple-choice questions, each having 5 answer choices?

27. How many ways can the letters in the word SAXOPHONE be arranged?

28. How many ways can the letters in the word CLARINET be arranged if the vowels must be kept together?

29. How many ways can the letters in the word MACHINES be arranged if all the consonants must be kept together?

30. How many ways can the letters in the word SANDWICH be arranged if the W, D, and C must be together and the vowels must be together?

31. How many ways can the letters in the word CAMPING be arranged if the vowels must be together and the consonants must be together?

32. There are 19 members of a church group. The group leaders must pick 10 members to go on a mission trip. How many ways can they pick the group if Dan and Ann must go but Charlie cannot go?