Math

Permutations and CombinationsYou 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

Math

Permutations and CombinationsHow 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

Math

Permutations and CombinationsAn 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

Math

Permutations and CombinationsCalculate 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?

Math

Permutations and CombinationsJamie 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

Math

Permutations and CombinationsSuppose 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?

Math

Permutations and CombinationsA 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?

Math

Permutations and CombinationsAt 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

Math

Permutations and CombinationsA 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?

Math

Permutations and CombinationsA 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.

Math

Permutations and CombinationsSuppose 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.)

Math

Permutations and CombinationsNumber 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.)

Math

Permutations and CombinationsFrom 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?

Math

Permutations and CombinationsLamar 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?

Math

Permutations and CombinationsSuppose 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

Math

Permutations and CombinationsUsing 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

Math

Permutations and CombinationsIn 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.)

Math

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

Math

Permutations and CombinationsDetermine 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.

Math

Permutations and CombinationsExpand 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

Math

Permutations and CombinationsA 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.

Math

Permutations and CombinationsJamie 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?

Math

Permutations and CombinationsSolve 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

Math

Permutations and CombinationsAmy, 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;

Math

Permutations and CombinationsA 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

Math

Permutations and CombinationsYou 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?

Math

Permutations and CombinationsIn 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.

Math

Permutations and CombinationsIn 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?

Math

Permutations and CombinationsHow 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.)

Math

Permutations and Combinations2. 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?

Math

Permutations and CombinationsYou 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?

Math

Permutations and CombinationsIf 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?

Math

Permutations and CombinationsIn 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.
*****

Math

Permutations and CombinationsAn 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?

Math

Permutations and CombinationsIf 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

Math

Permutations and CombinationsA 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?

Math

Permutations and CombinationsModel 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.

Math

Permutations and CombinationsUse 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.

Math

Permutations and CombinationsA 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

Math

Permutations and CombinationsA 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?

Math

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

Math

Permutations and CombinationsThe 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.)

Math

Permutations and CombinationsAt 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?

Math

Permutations and CombinationsA 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?

Math

Permutations and CombinationsThe 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!

Math

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

Math

Permutations and CombinationsA 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?

Math

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