Combinations and Permutations Statistics Probability Combinations and Permutations Questions At a restaurant, you can choose from 2 appetizers, 4 main courses, and 3 desserts. How many different meals, each consisting of one appetizer, one main course, and one dessert, can be created? In general, if you have #m# items of one type and #n# things of another type, how many possible ways can you choose one of each? You have created a (random) 5-digit password for your computer. A hacker tries to break in to your computer. What is the probability that he is successful on the first attempt? In how many ways can you arrange 5 books in a bookshelf? How do you calculate permutations on the TI-84? In how many ways can you rearrange the letters A, B, C, D, E? There are 7 children in a classroom. In how many ways can they line up for recess? What is a combination? What is the difference between combinations and permutations? There are 9 students in a club. Three students are to be chosen to be on the entertainment committee. In how many ways can this group be chosen? How do you calculate combinations on the TI-84? How can a tree diagram help you determine the number of possible ways in which selections can be made? How do you distinguish between whether should use a permutation and a combination for a given problem? Permutation and combination? In your own words, explain the difference between a permutation and a combination. Also, give an example of a problem whose solution is a permutation and an example of a problem whose solution is a combination.? If license plates have three numbers and three letters in any order, how many unique license plates can there be? What is a permutation? How many solutions does the equation A+B+C=5 have if A, B, and C are non negative integers? If there are 100 students in a school, how many unique classes of 25 students can be formed? You are dealt five cards from an ordinary deck of 52 playing cards. In how many ways can you get a full house and a five-card combination containing two jacks and three aces? Different 4 math books , 6 different physics books , 2 different chemistry books are to be arranged on a shelf. how many arrangement is possible if the books in particular subject must stand together ? In how many different ways can 6 classes be scheduled during a 6-period day? In how many different ways can you arrange the letters of the word INTERNET? In how many different ways can you arrange the letters of the word COMPUTER taking 4 at a time? In how many different ways can you arrange the letters of the word TRIGONOMETRY? In how many different ways can the 9 starters of a baseball team be placed in their positions? How many different two-digit numbers can be formed from the digits 3, 1, 4, and 5 (allowing reuse)? How many seven-digit phone numbers can be formed if the first digit cannot be 0 and repetition of digits is not permitted? The Board of Directors does not have assigned seats in the conference room. If there are 12 of them, seated at a round table, how many different seating arrangements are possible? Using the letters of the word YOUNG, tell how many different 5-letter combinations are possible if the first letter must be Y? I have one hundred students and want to form classes of 25 students, how many different groups of students can i have? In how many ways can the letters in the word INFINITY be arranged? How many distinguishable ways can the letter of the word SASSAFRAS be arranged using all the letters? Five people are to dine at a rectangular table but the host cannot decide on a seating arrangement in how many ways can the guests be seated? How many different words can be formed of the letters of the word MALENKOV so that no two vowels are together? How many permutations of five voters can be made? How many 3 letter permutations can be made from the letters COMPUTER? Supposed that a department contains 10 men and 15 women. How many ways are there to form a committee with six members if it must have more women than men? How many was can 10 people come in 1st, 2nd and 3rd place in a race once around the track? Ten elementary school students are eligible to be appointed to two positions: attendance taker and lunch counter. How many unique arrangements of these two positions are possible? How do you find the number of permutations of 5 CDs if you have a total of 23 CDs? How do you find the number of permutations of the first 13 letter of the alphabet taking 4 letters at a time? A test consists of 25 problems and students are told to answer any 15 of these questions. In how many different ways can they choose the 15 questions? How many ways are there to choose a committee of 5 people from a group of 15 people? In how many ways can 9 books be arranged on a shelf? In how many ways can 9 books be arranged on a shelf if a particular book must occupy the central position? Given 9 starting batters on a baseball team, how many batting orders are possible if the shortstop must bat first and the right fielder must bat fourth? How many arrangements are there of the letters in the word CURTAIN? At a party each guest shook hands with every other guest exactly once. There were a total of 105 handshakes. How many guest were there? A pizza place offers 3 different cheeses and 8 different toppings. In how many ways can a pizza be made with 1 cheese and 3 toppings? A pizza place offers 5 different cheeses and 10 different toppings. In how many ways can a pizza be made with 2 cheese and 3 toppings? In how many ways can a teacher arrange 4 students in the front row of a classroom with a total of 30 students? In how many ways can a teacher arrange 5 students in the front row of a classroom with a total of 23 students? How do you find the number of ways to listen to 4 different CDs from a selection of 15 CDs? A test consists of 30 problems and students are told to answer any 10 of these questions. In how many different ways can they choose the 10 questions? How many ways can you purchase 2 CDs if there are 3 to choose from, 4 cassettes if there are 4 to choose from, and 2 DVDs if there are 5 to choose from? How do you find the number of permutations in the word arithmetic? How do you find the number of ways to listen to 4 CDs from a selection of 8 CD? A pizza place offers 4 different cheeses and 10 different toppings. In how many ways can a pizza be made with 2 cheese and 3 toppings? A pizza place offers 4 different cheeses and 10 different toppings. In how many ways can a pizza be made with 1 cheese and 4 toppings? What is the number of numbers that can be made from the numbers two and three such that the number contains 4 digits? In a survey of 375 dog and cat owners, there were 215 dog owners and 193 cat owners. How many in the survey own a dog and no cat? If you have 20 dice (with 6 faces each), how many different numbers can you create putting the dice in one line and interpreting each face as a digit? How many arrangements of the letters in the word GRACIOUS both begin and end w/ a vowel? How do you evaluate 5(3P2)? How do you evaluate 5C2 + 5C1? In how many different orders can six colored blocks be chosen from a set of 23 different blocks? How many permutations are there of the letter in the word baseball? How many four–letter permutations can be formed from the letters of the word OHIO? How many seven–letter permutations can be formed from the letters of the word GIGGLES? How many ways can 5 people sit in row around a circular table? In how many ways can a committee of six be formed with two people from each country? Tabitha and Paul are in a video game room that consists of 10 games. If they only have enough money to play 6 games, how many ways can they play each of the 6 games once? A composition teacher needs to choose 10 students out of 15 to serve as rough draft reviewers. A group of 10 seniors, 3 juniors, and 2 sophomores have volunteered. How many different ways can the teacher choose 10 students? The student council advisor needs to appoint two council members to be officers: one president and one vice-president. Student council consists of six members. How many possible ways are there for the advisor to fill the offices? How many different two-person teams can be made from 6 people? How do you find the number of distinguishable permutations of the letters HONEST? How many different 3 people committees can be formed from a group of 25 people? From a class of 28 students, how many different ways can 4 students be selected to serve on the student council as president, vice president, secretary and treasurer? The boy's volleyball team has 24 players. If the coach chooses 9 boys to play at a time,how many different teams can be formed? Five cards are dealt from a standard deck of 52 cards. How many different 5-card hands will contain all hearts? Five cards are dealt from a standard deck of 52 cards. How many different 5-card hands will contain exactly 3 kings and exactly 2 aces? You have mixed up your locker combination again! You know it has the numbers 9, 7 and 23, but you are not sure of the order. What is the probability you get it open on the first try? How many ways can a baseball manager make a 9-player batting order from a group of 16 players? Question #d548a Question #4b3a7 Using the digits #1,2,3,4,5,6# as many times as you wish, how many #3# digits numbers can you make that are divisible by #5# ? A clerk has 4 different letters that need to go in 4 different envelopes. What is the probability that all 4 letters are placed in the correct envelopes? Question #a6eab Question #4cce4 Question #94b63 In poker, a 5-card hand is called two pair if there are two cards of one rank, two cards of another rank, and a fifth card of a third order of the cards doesn't matter (so, example, QQ668 and 68QQ6 are the same). How many 5-card hands are two pair? Question #ef342 In a card game using a standard 52 card deck, 4-card hands are dealt. What's the probability of being dealt 3 diamonds? In a waiting room are 10 seats. Three sisters want to sit together and there are three other people as well. In how many ways can the 6 people sit in the waiting room? We have three cars with four people in each car. If the car owner must occupy their own car, how many arrangements of the people are possible? A music lover has 28 songs and is able to make a playlist of 12 songs (order doesn't matter). How many different 12-song playlists can be made? Is it realistic and practical to make all of them? Question #3cd19 15 people apply for a job to be a trainee. Only 5 can be picked. In how many ways can a group of 5 trainees be picked? 43 antique cars are in a show, with 1st, 2nd, and 3rd prizes to be awarded. In how many ways can the awards be given? 1. How many 4-digit codes can be made if no digit can repeat? 2. How many ways can 5 bikes be displayed in a store window from a group of 12? Question #7023b Avril and Ben are surveying passing traffic, noting the number of occupants in each vehicle. Below is the table of results of their survey? Four men and four women have just six tickets in one row to the theater. In how many ways can they sit if the first person in the row is a woman and the people alternate woman,men? How many odd numbers are there, using the digits 5, 6, 7, 8, 9, 0, that are greater than 1,200,000 with the conditions a. no repetition and b. repetition? Answer the following questions with an explanation? How do we prove that #((n),(k))=sum_(l=k)^n((l-1),(k-1))#? How many lines are determined by 8 points, no more than 3 of which are collinear? How many triangles are determined by the same points if no more than 4 are coplanar? How many possible orderings are there of the letters: N, N, B, B? How do you find the number of distinct permutations possible with the letters of the word "degree" using all the letters? In how many ways can a committee of 4 be selected from 6 men and 8 women if the committee must contain at most 2 women? From all the permutations of 5 different letters from the 7 letters D, E, C, I, M, A, and L, how many begin and end with a consonant? How do you solve for #n# in #P(n,4)=30[C(n-1, 3)]#? A password is to consist of six lowercase letters. How many passwords are possible? In a 7 horse race, Bill thinks horses 1, 4, 6, will be the top 3 horses in the race, but not necessarily in that order. If Bill is correct, how many different outcomes are possible? Of a group of 50 students, 20 are freshmen, 10 are sophomores, 15 are juniors, and 5 are seniors. 5 members must be chosen. How many different committees can there be if there must be exactly one senior and exactly two freshmen on the committee? What are combinatorics in discrete mathematics? License plates are made using 3 letters followed by 2 digits. How many plates can be made if repetition of letters and digits is allowed? There are n #>=# 11 people. Set A must have 10 people. Set B must have 11 people. A person may belong to both A and B at the same time. How many ways can this be done? In the binary number system which is used in computer operations, there are only two digits allowed: 0 and 1. How many different binary numbers can be formed using at most four binary digits? In the binary number system which is used in computer operations, there are only two digits allowed: 0 and 1. If eight binary digits are used, how many different binary numbers can be formed? A binary code is a system of binary numbers with a fixed number of digits that are used to represent letters, numbers, and symbols. To produce enough binary numbers to represent all of the letters of our alphabet, how many binary digits must be used? From a deck of 52 cards, how many different four-card hands could be dealt which include one card from each suit? The prime factorization of 540 is 2 x 2 x 3 x 3 x 3 x 5. How do you find the number of divisors of 540 other than 1? If last year's champs, the Anows, must be in the first division and the current league leaders, the Bows, must be in the second division, in how many ways can the selection be made? A shelf holds seven mystery novels and eight biographies. Josie chooses either a mystery novel or a biography. Then Juan is to choose a mystery novel and a biography. In which case would Juan have the greater number of choices? Morse code is used to send messages. Each symbol is represented by a series of dots and dashes. Why is it sufficient to use at most five dots and/or dashes to represent any symbol? Morse code is used to send messages. Each symbol is represented by a series of dots and dashes. Would a maximum of four dots and/or dashes be sufficient? You have #n# pieces of pie to be given out to #k# people, and all #n# pieces are given out. How do you find a formula for the total number of ways to give out pie? A bag contains 1 red ball and 2 white balls. One ball is randomly selected from the bag and then returned. What is the probability that exactly one of the first five balls selected is white? The astrological configuration of a party with n guests is a list of twelve numbers that records the number of guests with each zodiac sign. How many different astrological configurations are possible for n = 100? There are 20 rabbits, 15 black and 5 white. You take one by one a rabbit. What's the probability of having at least 2 white rabbits next to each other? How many lines are determined by 8 points, none of which are collinear? In how many ways can 9 books be arranged on a shelf if 2 of them must be kept together? There are 2 identical boxes, 2 identical white balls, 1 red ball, and 1 blue ball. In how many different ways can we fill each box with exactly 2 balls? In how many different ways can we fill one box with 3 balls and the other with 1? From the digits 1, 2, 3, 4, 5, 7, 9, how many numbers of 3 digits can be formed if repetition is allowed in a number? Suppose that a committee of 4 is to be chosen from 6 married couples. In how many ways can this be done? Of the possible committees how many contain exactly 2 women? How many election outcomes in the race for class president are there if there are five candidates and 40 students in the class and no candidate receives a majority of the votes, meaning nobody gets higher than 20 votes? How many election outcomes in the race for class president are there if there are five candidates and 40 students in the class and exactly three candidates tie for the most votes? There's a deck of 52 cards. A five-card hand has three of a kind consists of 3 cards of the same rank, one card of another, and one card of another. How many different 3-of-a-kind hands are there? The director of a government agency has been given a list of 12 firms cited for unfair labor practices. Because of staff shortage and inefficiency, only one-fourth of these 12 can be charged. How many possible sets of 3 firms can be charged? The library is to be given 3 books as a gift. The books will be selected from a list of 18 titles. If each book selected must have a different title, how many possible selections are there? Question #1889a If we have the numbers 1, 2, 3, and 4, how many combinations of 4 digit numbers can we make? We're arranging 8 books on a shelf. How many ways can we arrange the books if the history, biology, and computer programming books (1 each) can't be together? Of the 6 courses offered by the music department at her college, Kay must choose exactly 4 of them. How many different combinations of 4 courses are possible for Kay if there are no restrictions on which 4 courses she can choose? If I had #N# fermions, how could I determine the number of ways I can place these into #g# distinguishable containers? For example, how could I determine how many ways I could place #54# electrons into #54# #p# orbitals? How do you write all permutations of the letters A, B, C, D if the letters B and C must remain between the letters A and D? There are 6 people in a group that walk into a restaurant. The only table open is a 4-person table. In how many different ways can 4 people be seated at the table if we don't care where the 4 people sit at the table? Chris has 25 songs in his library and wants to put 12 of them into a playlist. If he picks songs at random, how many different groups of songs can be created? Question #f2180 How many ways can an adviser choose 3 students from a class of 10? A spinner is divided into fourths and numbered 1 through 4. Jory spins the spinner and tosses a coin. What are all the possible outcomes? How many outcomes are in the sample space? If you roll a die three times, how many different sequences are possible? What's 4P4? Question #c4795 How many subsets are in the set {math, English, history, science}? The principal of the high school selects 4 Merit Scholars to attend a Town Council meeting. If there are a total of 12 Merit Scholars at the school, in how many ways can the students be selected? Question #e4412 How many three-letter sequences can be made from the letters in the word FORESAW? How many five-digit numbers can be formed by rearranging the digits in the number 93,218? A baby presses the ten numbers (zero through nine) on a phone dial pad once each. How many different number sequences could she have dialed? Katelyn was asked to hang 4 student paintings in a row on the wall. How many different ways could she arrange them? Four people are boarding onto a mostly full airplane. There are 12 open seats, 2 of which are aisle seats. We want at least one of the four passengers to sit in an aisle seat. In how many ways can the 4 people sit? Evaluate #""^3C_1# ? 11 books, all with different titles, are to be arranged on a shelf. 4 are history books and one of them needs to be in the middle of the arrangement. 2 are math books and they need to be on the ends. How many different ways can they be arranged? Verne has 6 math books to line up on a shelf. Jenny has 4 English books to line up on a shelf. In how many more orders can Verne line up his books than Jenny? Find the total number of ways in which a beggar can be given at least one rupee from four 25paise coins,three 50paise coins & 2 one rupee coins ? (1rupee=100paise) In the school cafeteria, students choose their lunch from 3 sandwiches, 3 soups, 4 salads, and 2 drinks. How many different lunches are possible for a student who chooses exactly 1 sandwich, 1 soup, 1 salad, and 1 drink? In how many ways can the letters in the word ALLERGENS be arranged? Question #db687 Professor Snarff says, "You may work these six problems in any order you choose." There are 100 students in the class. Is it possible for all 100 students to work the problems in a different order? Simplify #(C_2^7xxC_3^6)/(C_3^7xxC_4^5)#? How many ways can a committee of 3 men and 2 women be chosen from a pool of 8 men and 7 women? A train schedule shows that 2 days per week one train departs, 3 days per week two trains depart, and 2 days per week three trains depart. How many different ways can the schedule be made? Question #c0154 What's 8P3? What's 7C3? And what do they mean? What is the value of #4P4#? A smoothie shop offers drinks with 5 types of whole fruit, 4 types of juice, and 3 flavors or yogurt. How many smoothie combinations are possible? Is selecting the batting order in a baseball game a permutation or combination? How do you evaluate #""_7P_3#? How do you evaluate #""_7P_4#? How do you evaluate #""_7P_7#? How do you evaluate #""_8C_3#? How do you evaluate #""_8C_5 * _7C_3#? How many different ways can 6 books be placed on a shelf? How do you simplify #""_10P_8#? How many different arrangements can be made with the letters in the word POWER? 9 students volunteer for a committee. How many different 7-person committees can be chosen? How do you evaluate #""_10C_8#? How many ways can 6 different books be arranged on a shelf? A deli offers 3 different kinds of bread and 8 different kinds of toppings on its submarine sandwiches. How many different sandwiches are possible? How many different student body governments are possible if there are 4 seniors, 5 juniors, and 3 sophomores running for the student body offices of senior class president, junior class president, and sophomore class president? In how many different orders can Debbie, Brigitte, and Adam wait in line in the school cafeteria? What is the probability that they will be in alphabetical order? In a club there are 10 women and 7 men. A committee of 6 women and 4 men is to be chosen. How many different possibilities are there? While on vacation, Sandra wants to buy 2 wallets. There are 7 different patterns she can choose from. In how many ways can Sandra choose 2 different wallets? How many different permutations can you get from the letters in the word INVISIBILITY? Francine is deciding which after-school clubs to join. She has time to participate in 3 out of 9. How many different ways can Francine choose which 3 clubs to join? How do you find #""_11P_3#? A pizza place offers 5 different cheeses and 10 different toppings. In how many ways can a pizza be made with 3 cheese and 6 toppings? If Missy has 8 identical tulip plants and 4 identical daisy plants, in how many ways can she use the plants to line the walkway? How many outcomes are possible when flipping 4 coins? I have 5 blue socks, 3 red socks, 4 green socks. I take two socks from the drawer. How do you list all the possible outcomes for the two socks? The camera club has five members, and the mathematics club has eight. There is only one member common to both clubs. In how many ways could a committee of four people be formed with at least one member from each club? In how many distinct ways can the letters of the word STATES be arranged? How many three-digit numbers with distinct digits can be formed using the digits 1, 2, 3, 5, 8, and 9? What is the probability that both the first digit and the last digit of the three digit number are even numbers? In how many ways can the digits in the number 9,164,461 be arranged? How may permutations of the word "spell" are there? How many ways can you choose a set of 9 pencils from a selection of 10? How many committees of 3 can be formed from a group of 9? How many five-digit numbers can be formed using the digits 0, 1, 2, 3, 4 5, 6, 7, 8, 9, if repetitions of digits are allowed? How do you evaluate #""_14P _ { 5} #? Question #a504d With the word Quicker, how many ways can we arrange the letters if U and I can't be together? What is the recurrence formula for #K_n#? #K_n# is the number of strings (#a_1,a_2,...,a_n) with words from set {0, 1, 2} under the following conditions. What is the recurrence formula for #L_n#? #L_n# is the number of strings (#a_1,a_2,...,a_n#) with words from set {#0, 1, 2#} without any adjacent #0# and #2#. Out of a batch of #60# computers, #5# are damaged. If two computers are chosen at random from the #60#, what is the probability that both are damaged? Five of the 100 digital video recorders (DVRs) in an inventory are known to be defective. What is the probability you randomly an item that is not defective? Barbara and John and six other people go through a doorway one at a time. Find the number of ways in which the eight people can go through the doorway if John goes through the doorway after Barbara? The number of ways of distributing 10 identical balls in 4 distinct boxes is? case 1 : no box should be empty. case2 : atmost three boxes ca be empty. Question #c1283 What's 8P8? Solving Permutations and Combinations.Solving for variable.Find the value of r in 6Pr = 30? 5 letters in each of 3 rings of a lock are printed. If the lock can be opened by only one permutation of three letters, then find the number of permutations by which the lock cannot be opened? ps: by locks it meant those locks we have in ourbriefcase If nPr =nCr..... x. ,then what is the value of x? How many permutations are there for the word numbers? 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