What principle of counting would you use in each of the following situations? + You have to count the number of three-letter initials. Counting ways to choose a dessert from the menu with three kinds of cakes and four kinds of pies. A. Addition principle B. Inclusion - exclusion principle You have to count the number of positive integers less than 100 that are divisible by 3 or 5. C. Multiplications principle * Counting the total number of bit strings of length 5. * You have to count the number of different 4-digit pin codes.

Q: In how many ways can n couples sit at a round table such that no couple is sitting opposite each…

A: The solution is given as follows

Q: 4. At a deli there is a lunch special where you can make a sandwich from picking 1 ingredient from…

A: From the four types of bread, one can be chosen, so the number of ways is From the five types of…

Q: Use​ permutations, combinations, the fundamental counting​ principle, or other counting​ methods, as…

A: Given data: The total numbers of students are n=21. The numbers of student in the first group are…

Q: A government agency hires you to provide consulting on new rules regarding vehicle license plates.…

A:

Q: Q2. Count the number of seven-card hands that can be drawn from a standard deck such that the hand…

A:

Q: 5.) There are three positions of programmers in a bank. Position I is the daytime programming…

A: We have three positions which is to filled with 15 candidates So for first position we have 15…

Q: Many states have a lottery game, usually called Pick-4, in which you pick a four-digit number such…

A: Introduction: There are 4 digits to be selected for the game. Each digit can be any one between 0…

Q: Many states have a lottery game, usually called Pick-4, in which you pick a four-digit number such…

A: i) All four digits are unique The probability is determined as below,…

Q: A computer system uses passwords that have six characters, and each character is one of the 26…

A: Given that there are 26 character and 0-9 number

Q: 2. KC is selling siomai of different kinds: Pork (p), chicken (c), and beef (b). and shake which…

A: We wiil show  different ways of showing the possible combination in this situation as following.

Q: A textbook search committee is considering 12 books for possible adoption. The committee has decided…

A:

Q: nfirmation code consists of five letters followed by two digits, all of which can be repeated. Which…

A: For selecting 5 letters out of 26  we need combinations  For selecting 2 numbers out of 9 also we…

Q: In a survey of 1244 families conducted by a marketing agency in a particular city, the following…

A: Answer

Q: What is p(3, 2)? [Hint: Each sample of size 6 is equallylikely to be selected. Therefore, p(3, 2) 5…

A:

Q: How many 5 card hands from a standard deck have at least one card of each suit?…

A: For a five-card hand to have one card in each suit, it must be the case that the hand contains two…

Q: The grades of students in a Finite Mathematics course at a certain university are determined by…

A:

Q: 2) Allowing (or requiring) users to use numerical digits (including 0) and one of 31 "special…

A: Introduction: Considering the lower- and upper-case alphabets to be two different characters, total…

Q: A textbook search committee is considering 12 books for possible adoption. The committee has decided…

A:

Q: A textbook search committee is considering 11 books for possible adoption. The committee has decided…

A:

Q: The license plates in a certain country consist of 7 different digits, and the first one cannot be…

A:

Q: What is the main difference between a situation in which the use of the permutations rule is…

A: The major and main difference in the use of permutation rule and the combination rule is ordering.…

Q: The password consists of alphanumeric characters (i.e. letters or numbers) that distinguish between…

A: Introduction: According to the combination rule, if r distinct items are to be chosen from n items…

Q: Determine the sum of the first 600 whole numbers. 1 + 2 + 3 + ... + 599 + 600  = ______. (Hint: Use…

A: using formula,

Q: 15. A rug manufacturer has decided to use five co rug, only four spindles can be used. In…

A: Given that -A rug manufacturer has decided to use five compatible colors in her rugs. However, in…

Q: Consider a horse race with 8 horses. Explain how the fundamental principle of counting or the…

A:

Q: If we have a population of 9 objects, in how many ways may we select a sample of 5 objects from the…

A: The population size is N = 9 Sample size is n = 5

Q: 1. The Fundamental Counting Principle says that if one event can occur in m ways and a second event…

A: To fill in the blanks.

Q: 4. How many cards must you pick from a standard 52-card deck to be sure of getting at least 1 red…

A: As per the Bartleby guildlines we have to solve first question and rest can be reposted... Given…

Q: Answer the following question using the appropriate counting​ technique, which may be either…

A:

Q: A textbook search committee is considering 14 books for possible adoption. The committee has decided…

A: Consider the given information.

Q: A PIN-number for a credit card consists of a sequence of 4 digits chosen from the set…

A: Given the set {0,1,2,3,4,5,6,7,8,9} We find the 4 digits different PIN number

Q: How many ways to distribute 10 pencils (indistinguishable), 15 erasers (distinguishable), and 20…

A: From the given information, Total number of person =10 Number identical pencils =10 Total number of…

Q: How many distinct permutations can be formed from all letters of the word “SOCIOLOGICAL”? Moreover,…

A: Consider the given word SOCIOLOGICAL. The total number of letters is 12 N=12. Out of these, there…

Q: 3​-digit counting numbers can be constructed from the digits {1,2,3,4} if repetition is not allowed.…

A:

Q: A bag contains 7 black and 9 white balls. In how many ways can we draw from the bag groups of 4…

A:

Q: 5) How many different passwords are possible? If a cell phone's password consists of eight…

A: Given: Considering 0 to 9, there are 4 even numbers and 4 odd numbers. In alphabets there are total…

Q: Many states have a lottery game, usually called Pick-4, in which you pick a four-digit number such…

A:

Q: 4. In some states,license plates consist of 3 letters followed by 2 or 3 digits (for example, JWK-…

A: Given: 4) License plates consist of 3 letters followed by 2 or three digits. To find: How many such…

Q: A local college is forming a seven-member research committee having two administrators, three…

A: Given The number of members in contention for the committee are following  The number of…

Q: Use permutations,combinations, the fundamental counting principle, or other counting methods, as…

A: From the information, there are 21 students in the class and they are divided in to 3 sets 1st set 3…

Q: How many words can be formed by permutation of the letters of the word DEPRESSION such that each…

A:

Q: A selection of items chosen from a group in which order is not important. O Permutation O…

A: 1) Permutation: The number of possible arrangements in a set when the order of the arrangements…

Q: In a state pick 4 lottery game, a bettor selects four numbers between 0 and 9 and any selected…

A: Given information In a state pick 4 lottery game, a bettor selects four numbers between 0 and 9 and…

Q: There are 6 periods in each class day in a school. How many ways can one organize 5 subjects such…

A:

Q: Two digits are selected with replacement from the digits 1, 2, 3, 4, 5, and 6. How many…

A: There are 6 digits given. And the trial is with replacement. So we can pickt the first digit in 6…

Q: A combination lock uses three numbers between 1 and 36 with repetition, and they must be selected in…

A: 1.) Here, three numbers are used between 1 to 36 with repetitions. The all possible ways in which a…

Q: Find the total number of permutations of the word 'ASSASSINATION', where all vowels are ALWAYS…

A: We have to find the number of ways

Q: Use​ permutations, combinations, the fundamental counting​ principle, or other counting​ methods, as…

A: Given Data: The number of students in the class is: n=15 The number of students in the first set is:…

Q: Determine how many 3​-digit counting numbers can be constructed from the digits {1,2,3,4} if…

A: Determine how many   3​-digit  counting numbers can be constructed from the digits  {1,2,3,4} if…

Q: Find the number of ways to select 12 objects with repetition from 5 distinct types of objects with…

A:

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.