Five people plan to meet after school, and if they all show up, there will be one group of five people. However, if only two of them show up, in how many ways is this possible?

Q: In certain state, license plates each consist of 3 letters followed by 3 numbers. (a) How many…

A: Since you have asked multiple subparts, we will solve the first three subpart questions for you. If…

Q: A casting director wishes to find one male and one female to cast in his play. If he plans to…

A:

Q: On a ballot, the candidates for each office are listed together under the office for which they are…

A: Number of candidates in one office is 5. Number of candidates in another office is 3.

Q: Suppose you are taking a bus trip from your home in Florida to California. There are seven different…

A: Given that we are taking a bus trip from your home in Florida to California. There are seven…

Q: In how many ways can six different books, four of which are math books, be arranged on a shelf if…

A:

Q: Elvis has 12 close friends. How many different combinations of 5 of them may be invited for dinner…

A: Total number of friends = 12 Number of friends she can invite = 5

Q: How many ways are there to choose 20 co-op candidates out of 30 students to send to work at the same…

A: For the solution follow the next step.

Q: The Student Council at a certain school has ten members. Four members will form an executive…

A: Given,  The student council at a certain school has ten members.

Q: Suppose a certain combination lock requires three selections of numbers, each from 1 through 25 (b)…

A:

Q: A one-topping pizza consists of choosing a crust, a type of cheese, and one topping. If there are 4…

A:

Q: A club with ten members is to choose three​ officers: ​ president, vice-president, and​…

A:

Q: At a lottery, 100 tickets were sold and three prizes are to be given. How many possible outcomes are…

A: Given :At a lottery, 100 tickets were sold and three prizes are to be given. How many possible…

Q: A group of Mathematics faculty at the local college consists of 10 women and 10 men. Five people are…

A: Given  No of men = 10 No of women = 10 We need to select 5 people

Q: Given a deck of 52 playing cards, in how many ways can a hand of 5 cards be dealt such that exactly…

A:

Q: If there are nine distinct items 3 at a time, how many permutations will there be

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Q: how many ways can 5 textbooks, 3 coffee table books and 2 novels be arranged if the textbooks must…

A: This question is from permutation We have to calculate, in how many ways 5 textbooks, 3 coffee table…

Q: In one state, each automobile license plate shows three letters followed by two digits, or two…

A: The number of letters in alphabet is 26. The number of digits from 0 to 9 is 10.

Q: At a local restaurant, a dinner special consists of choosing a salad, an entree and a dessert. If…

A: If there are 3 choices for salad, 6 choices for the entree, and 4 choices for dessert. At a local…

Q: A family has nine children. If this family has exactly five boys​, how many different birth and…

A: Given,A family has 9 childrens

Q: In a certain get together, there was a basket of fruits for every three guests, a basket of cookies…

A: Let the number of fruit baskets be x, the number of cookies baskets  be y and the number of chips…

Q: In one class 18  students play basketball, 14 students play soccer and 10 students play volleyball.…

A: You can solve this question using the Venn diagram.

Q: Suppose you have a set of cups and saucers which are red, orange, green, light blue, dark blue, and…

A: Number of different coloured coffee cup=6 Number of different coloured saucer=6

Q: how many ways can four doctors and three nurses be seated in a row if the doctors and nurses are to…

A: Given that :  D represent doctors .  N represents nurses.  Arrangement in which Doctors and Nurses…

Q: Three members of an organization volunteered to serve as President, Treasurer and Secretary. In how…

A:

Q: A coffee shop offers five different flavors of coffee and three flavors of doughnuts. How many…

A:

Q: there are 651 6th grade students at a school, and three out of every seven of them play a sport, how…

A: Given   Number of 6th grade students : 651   If 3/7 plays sports,    Then who don't play a sports…

Q: Three married couples have purchased tickets for a play. Spouses are to be seated next to each…

A: Given :  Three married couples purchased tickets.                 To find  :  How…

Q: Five people plan to meet after school, and if they all show up, there will be one group of five…

A: Five people plan to meet after school. We have to find the number of ways if three of them show up.

Q: In how many ways can 7 women and 7 men partner up for ballroom dancing, if each person has to dance…

A: The number of ways to select r objects from n objects is computed by using the formula of…

Q: The board of directors of a corporation must select a president, a secretary, and a treasurer. In…

A: Given that there are total 14 members.    A president, a secretary, and a treasurer represent 3…

Q: (a) In a certain state, license plates have two letters followed by four digits. How many such…

A:

Q: There are 10 people to be selected from. How many committees are possible?

A: Here use combination

Q: The newest cars have 12 different accessories and the buyer pays for each one separately.  If a…

A: Given, The newest cars have 12 different accessories A buyer wants to buy four accessories

Q: A club with eleven members is to choose three​ officers: ​ president, vice-president, and​…

A: A club with eleven members is to choose three​ officers: ​ president, vice-president, and​…

Q: A student taking an examination is required to answer exactly 10 out of 15 questions. in how many…

A:

Q: A company has 10 software engineers and 6 civil engineers. In how many ways can they be seated…

A:

Q: How many ten-digit telephone numbers are possible if the first three digits must all be different?

A: Given,total no.of digits=10  (0 to 9)

Q: coffee shop offers 14 different types of flavor shots. If a customer can choose any number of flavor…

A: Given a coffee shop offers 14 different types of flavor shots.

Q: how many hands of 33 cards can be made, where all cards are of the same suit?

A:

Q: A man has eight shirts and five ties. Assuming that they all match, how many different shirt-and-tie…

A: Given,            A man has eight shirts and five ties.

Q: Complete task from image

A:

Q: The board directors of a corporation must select a president, a secretary, and a treasurer. In how…

A: We will use arithmetic method to find solution to the problem.

Q: A student is given a reading list of ten books from which he must select two for an outside reading…

A: Given that the student has a list of 10 books from which he has to select 2 books

Q: A Maryland automobile license plate consists of three letters followed by three numbers.  How many…

A: As per bartleby guidelines only one question should be answered once, please upload each question…

Q: . a) How many ways can 6 people be lined up to get on a bus? o) If a certain 3 persons insist on…

A:

Q: If you pick 4 cards without replacement from a standard deck of 52 cards, how many different…

A:

Q: If there were to be 15 boys and 13 girls at a party and the host wanted each to be given exactly…

A:

Q: Twenty automobiles enter a race. Eight are made by manufacturer A, seven by manufacturer B, and the…

A: Introduction: Total number of automobiles is 20. Number of cars made by Manufacturer A is 8. Number…

Q: Suppose you have 11 books and you randomly pick 3 to take on vacation with you. How many ways can…

A: To count the number of possible selections

Q: A school dance committee is to consist of 2 freshmen, 3 sophomores, 4 juniors, and 5 seniors. If 6…

A:

Counting Principles

In statistics, the counting principle can be said to be the concept in which the quantity of an item is determined. There can be a single item, or a group of items, or items that are related to each other. In every possible set of items, the quantity of the possible item groups or their sorting measures can be determined with counting principles.