Permutations and Combinations Questions and Answers

You are playing a card game. If you pull an Ace you win $26, if you pull the King of hearts you win $204, if you pull a jack or a queen you win $13, all other pulls you lose. What price should you be charged to make this a fair game? $8 $7 $6 $5

How many 3-digit numbers greater than 600 can be formed using digits 2, 3, 4, 5, 6, 7 (repetitions are allowed)? (You will be asked to show your work on the last question of this assignment) 120 36 72 20

An environmental agency is analyzing water samples from 80 lakes. Five of those lakes are polluted. If 6 lakes are selected at random from the sample, how many ways could one polluted lake and 5 non-polluted lakes be chosen? (You will be asked to show your work on the last question of this assignment) 201,359,550 300,500,200 103,680 86,296,950

Calculate the number of permutations or combinations in each problem below. A teacher is creating groups for a project with 3 students in each group out of a total of 12 students. How many different combinations are possible? How many possible ways can a group of 9 people line up to wait for a music concert?

Jamie is practicing free throws before her next basketball game. The probability that she makes each shot is 0.6. If she takes 10 shots, what is the probability that she makes exactly 7 of them? Round your answer to three decimal places. Select the correct answer below: 0.200 0.215 0.234 0.251

Suppose you are asked to list, in order of preference, the three best movies you have seen this year. If you have seen 6 movies in the past year, in how many ways can the three best be chosen and ranked?

A large fast-food restaurant is having a promotional game where game pieces can be found on various products. Customers can win food or cash prizes. According to the company, the probability of winning a prize (large or small) with any eligible purchase is 0.177. Consider your next 37 purchases that produce a game piece. Calculate the following: Express your answer as a decimal with 4 decimal places. a) What is the probability that you win 6 prizes? b) What is the probability that you win more than 9 prizes? c) What is the probability that you win between 6 and 8 (inclusive) prizes? d) What is the probability that you win 3 prizes or fewer?

At Papa John's you are deciding on what you want for dinner. The pizza offers 8 different meats, 4 different cheeses, 3 different crust types and 2 different sauces. How many different pizzas do you have to choose from? (Hint: Use a list, tree diagram, or Fundamental Counting Principle.) 51,000 32 192 40,320

A restaurant lunch special allows the customer to choose two vegetables from the following group. corn carrots arugula peppers cauliflower kale fiddleheads broccoli spinach squash How many outcomes are possible if the customer chooses two different vegetables?

A machine that manufactures automobile pistons is estimated to produce a defective piston 1% of the time. Suppose that this estimate is correct and that a random sample of 80 pistons produced by this machine is taken. Answer the following. (If necessary, consult a list of formulas.) (a) Estimate the number of pistons in the sample that are defective by giving the mean of the relevant distribution (that is, the expectation of the relevant random variable). Do not round your response. (b) Quantify the uncertainty of your estimate by giving the standard deviation of the distribution. Round your response to at least three decimal places.

Suppose that 55% of all babies born in a particular hospital are girls. If 7 babies born in the hospital are randomly selected, what is the probability that fewer than 2 of them are girls? Carry your intermediate computations to at least four decimal places, and round your answer to two decimal places. (If necessary, consult a list of formulas.)

Number Two: You have 3 piles of cash each containing $100. You have 6 other piles of cash containing distinct amounts of dollars. None of the 6 contain $100 or contain an amount the same as any of the other piles. You have 12 friends. You are instructed to give a friend a pile of cash and then give that friend no more piles. (Each friend will get at most one pile). How many ways can you give away the piles of cash? (You do not get a pile in this problem.)

From a collection of 51 store customers, 3 are to be chosen to receive a special gift. How many groups of 3 customers are possible? (b) 52 athletes are running a race. A gold medal is to be given to the winner, a silver medal is to be given to the second-place finisher, and a bronze medal is to be given to the third-place finisher. Assume that there are no ties. In how many possible ways can the 3 medals be distributed?

Lamar is customizing his next pair of basketball shoes. The following table shows the design components and how many options he has for each. How many different shoe combinations can Lamar create?

Suppose a password must consist of two letters followed by three digits. Repeated characters are allowed. A password of this type is chosen at random. What is the probability that the password does not have any vowels? 0.44 0.65 0.20 0.85

Using the digits 1, 2, 3, 4, 5, 6, 7, 8 we can form 8! (= 40320) 8-digit numbers in which the eight digits are all distinct. For 1 ≤ k≤ 40320, let a denote the kth number if these numbers are arranged in increasing order. 12345678, 12345687, 12345768, ..., 87654321; That is, a₁ = 12345678, a2 = 12345687,..., a40320 = 87654321. Find a2009-a2008 9

In a certain lottery, you must correctly select 5 numbers (in any order) out of 36 to win. You purchase one lottery ticket. What is the probability that you will win? The probability of winning is (Use scientific notation. Use the multiplication symbol in the math palette as needed. Round to the nearest hundredth as needed.)

Three students have to give a speech in class today. In how many different orders can they give their speeches?

Determine whether the following problem involves a permutation or a combination and explain your answer. How many different 7-letter passwords can be formed from the letters S, T, U, W, X, Y, and Z if no repetition of letters is allowed? Choose the correct answer below. ..... OA. The problem involves a permutation because the order in which the letters are selected does matter. OB. The problem involves a combination because the order in which the letters are selected does matter. OC. The problem involves a permutation because the order in which the letters are selected does not matter. OD. The problem involves a combination because the order in which the letters are selected does not matter.

Expand the polynomial using the Binomial Theorem. (b + a)6 b6 +6b6a+15b4a2 +15b2a4 +6ba6+a6 a6+6a5b+ 20a³b3 + 30a2b4+6ab5+b6 b6+q6 b6 +6b5a +6ba5+ a6 a6+6a5b + 15a4b2+ 20a³b3 + 15a2b4+6ab5+b6

A restaurant offers the following limited lunch menu. Ham, Chicken, Fish Main Courses Vegetables Peas, Squash, Cauliflower, Eggplant Beverages Coffee, Tea, Milk, Soda, Shakes Desserts Ice Cream, Brownies If one item is selected from each of the four groups, in how many ways can a meal be ordered? CO There are ways a meal can be ordered.

Jamie is joining a music club. As part of her 4-CD introductory package, she can choose from 12 rock selections, 10 alternative selections, 7 country selections and 5 classical selections. If Jamie chooses one selection from each category, how many ways can she choose her introductory package?

Solve the problem by applying the Fundamental Counting Principle with two groups of items. An apartment complex offers apartments with four different options, designated by A through D. A number of bedrooms (one through four) B = number of bathrooms (one through three) C = floor (first through fifth) D= outdoor additions (balcony or no balcony) How many apartment options are available? A) 120 B) 16 C) 14 D) 240

Amy, Jean, Keith, Tom, Susan, and Dave have all been invited to a birthday party. They arrive randomly and each person arrives at a different time. In how many ways can they arrive? In how many ways can Jean arrive first and Keith last? Find the probability that Jean will arrive first and Keith will arrive last. A) 720; 24; 30 B) 120; 10; C) 120; 6; 20 D) 720; 15;

A restaurant offers a choice of 4 salads, 10 main courses, and 4 desserts. How many possible 3-course meals are there? A) 18 B) 40 C) 160 D) 320

You are taking a multiple-choice test that has 7 questions. Each of the questions has 5 answer choices, with one correct answer per question. If you select one of these choices for each question and leave nothing blank, in how many ways can you answer the questions?

In the following exercises, does the problem involve permutations or combinations? Explain your answer. It is not necessary to solve the problem. How many different user ID's can be formed from the letters W, X, Y, Z if no repetition of letters is allowed? A) Combinations, because the order of the letters does not matter. B) Permutations, because the order of the letters matters.

In the board game Clue, the object of the game is to determine the which character is the murderer, which weapon was used and in which room the murder took place (e.g., "Colonel Mustard with the Candlestick in the Library"). There are 6 different characters, 6 weapons, and 9 rooms. How many different outcomes are possible?

How many different ways could three distinct days of the week be chosen so that at least one of them begins with the letter St The number of ways is (Simplify your answer.)

2. Does the problem involve permutations or combinations?. The matching section of an exam has 3 questions and 7 possible answers. In how many different ways can a student answer the 3 questions, if none of the answer choices can be repeated?

You need to create a new password for your school account. It needs to be of the form: 4 numbers (0-9) followed by 3 letters. The numbers can repeat. The letters can repeat. How many different passwords can be created?

If there are n₁ of type 1, n₂ of type 2, and so on, for r different types, then the number of distinguishable permutations is calculated using the following formula. A shelf stocker at a local grocery store has 2 varieties of brand A frozen dinners, 2 varieties of brand B frozen dinners, and 4 varieties of brand C frozen dinners. Complete parts (a) through (c) below. (a) In how many distinguishable ways can she stock the shelves if the dinners can be arranged in any order?

In a race in which eight automobiles are entered and there are no ties, in how many ways can the first three finishers come in? There are ways for the first three finishers to come in. *****

Evaluate the expression. 12P3 12P3 = (Simplify your answer.)

An ice cream store sells 26 flavors of ice cream. Determine the number of possible 6-dip sundaes. How many 6-dip sundaes are possible if order is to be considered, and no flavor can be repeated?

If the n objects in a permutations problem are not all distinguishable-that is, if there are n₁ of type 1, n₂ of type 2, and so on, for r different types-then the number of distinguishable permutations is given by n!/n1!n2!....nr! How many permutations are possible using the 6 letters in the word WARSAW? The number of possible permutations is

Find the value of 7C3 O 24 0 210 O 35 O 5,040

A person going to a party was asked to bring 2 different bags of chips. Going to the store, she finds 12 varieties. How many different selections can she make?

Model with Math Joy added 26 new contacts to her phone list. She now has a total of 100 contacts. Let c represent how many contacts Joy had on her phone list before she updated it. Write an equation and solve for c.

Use permutations to solve. In a club with 24 members, how many ways can the club elect a president and a treasurer? Substitute values into the formula for npr.

A pizza parlor offers a choice of 12 different toppings. How many 5-topping pizzas are possible? (no double-orders of toppings are allowed) Your answer is: possible pizzas

A school dance committee is to consist of 2 freshmen, 3 sophomores, 4 juniors, and 5 seniors. If 5 freshmen, 9 sophomores, 9 juniors, and 7 seniors are eligible to be on the committee, in how many ways can the committee be chosen?

Find the number of different ways that an instructor can choose 3 students from a class of 11 students for a field trip.

The table to the right categorizes 20 senators as to political party and gender. One member is chosen at random. In how many ways can the chosen person be a woman or a Democrat man? There are 1680 senators that are a woman or a Democrat man. (Type a whole number.)

At a charity benefit with 25 people in attendance, three $50 gift certificates are given away as door prizes. Assuming no person receives more than one prize, in how many different ways can the gift certificates be awarded?

A computer user has downloaded 18 songs using an online file-sharing program and wants to create a CD-R with 13 songs to use in his portable CD player. If the order that the songs are placed on the CD-R is not important to him, how many different CD-Rs could he make from the 18 songs available to him?

The Poisson probability formula is shown to the right, where X is the number of times the event occurs and λ is a parameter equal to the mean of X. This distribution is often used to model the frequency with which a specified event occurs during a particular period of time. P(X=x) = e Suppose that a hospital keeps records of emergency room traffic. These records reveal that the number of patients who arrive between 4 P.M. and 5 P.M. has a Poisson distribution with parameter λ = 3.6. Complete parts a through c. XXXXX a. Determine the probability that, on a given day, the number of patients who arrive at the emergency room between 4 P.M. and 5 P.M. is exactly 5. P(X= 5) = (Round to four decimal places as needed.) 12x X!

In how many ways can 3 students from a class of 12 be chosen for a field trip? Your answer is :

A school committee consists of 3 sophomores, 4 juniors and 5 seniors. 9 sophomores, 12 juniors and 9 seniors are eligible to be on the committee. In how many ways can this be done?

A pizza parlor offers a choice of 16 different toppings. How many 6-topping pizzas are possible? Your answer is: