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

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: If there is a bird in every branch, there will be an excess bird not on the branch but if there will…

A: Here, it is given to us that: There is a bird for every branch, and if each bird sits on one branch…

Q: One semester in a chemistry class, 14 students failed due to a poor attendance, 24 failed due to not…

A: This Question can be easily solved using Venn Diagram

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

A:

Q: At an assembly, 8 out of the first 20 students who entered the gym were wearing grey shoes. Based on…

A:

Q: In how many ways can a hostess select 6 luncheon guests from 10 women, if she is to avoid having a…

A:

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: In how many ways can 3 boys and 3 girls sit in a row if the boys and the girls are each to sit…

A: Given,no.of boys=3no.of girls=3total no.of peoples=6

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

A: Given: The total number of cards in a deck is 52. The total number of the numbered cards in a deck…

Q: In how many ways: a. Can 8 people be lined up to get on a bus? b. Can they be seated if 4 specific…

A: Total persons  = 8 people a) There are 8 people, there will be 8 places to arrange (here order will…

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

A:

Q: A clothing store has 13 shirts in 4 sizes: small, medium, large, and extra-large for sale. If it has…

A: Number of ways of selling two small shirts is 2! = 2 Number of ways of selling three medium shirts…

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

A:

Q: In how many ways can president, vice-president, and secretary be chosen from a group of 20 people,…

A: Ways of selecting some fixed number of people from given set of number is done by simp0le counting.…

Q: six people to meet after school, and if they all show there will be one group of six. However if…

A: Given that, Six people to meet after school. If they all show up, there will be one group of six.…

Q: Assuming that no one can hold more than one office, how many selections are possible?

A: select a president, vice-president, secretary, and treasurer out of a club with 15 members.  Here…

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: In how many ways can 11 people be seated in a row of 11 chairs if Janet insists on sitting in the…

A:

Q: In a standard deck of 52 cards and 4 suits, how many cards have to be picked to be sure that at…

A:

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

A: Total number of member(n)=5 , Total number of people showing up the meeting(r)=2 number of…

Q: In how many ways can 10 people be seated in a row of 10 chairs if Janet insists on sitting in the…

A: The main objective is to find the permutations for the given problems.

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

A:

Q: A group of 30 people have been trained as astronauts to go on the first mission to Mars. How many…

A: Given that, The total number of people in the group is 30. And, a crew of six people to go on a…

Q: in how many ways can a hand of 5 cards be dealt such that 2 are black and 3 red cards?

A: Given:  There are 52 cards on the deck. There are 26 red and 26 black cards on the deck. Formula…

Q: (a) If a student must answer 8 of 12 questions on an examination, how many different selections of…

A: Given:  A student must answer 8 of 12 questions on an examination  To find:a) The different…

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

A: Here use combination

Q: 1. In your drawer, there are 6 identical pairs of purple socks, 7 identical pairs of polka dot…

A:

Q: There are five people at a volleyball tournament. In how many ways can a team of three be chosen?

A: The number of ways r items can be chosen out of n items is equal to C(n,r) . The formula for C(n,r)…

Q: Each employee at a large company is to be issued a computer ID code that consists of three letters…

A: From the given information, Total number places in the employee ID that needs to filled up =6 Total…

Q: In how many ways can three dogs, four cats, four rabbits and two pigs be arranged in a row so that…

A: Given,no.of dogs=3no.of cats=4no.of rabbits=4no.of pigs=2

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: In a group of 6 boys and 4 girls, 4 children are to be selected. In how many ways can they be…

A: The number of ways in which r different items can be selected from n different items, can be given…

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

A:

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

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: In a group of 4 people, is it possible for each person to have exactly 3 friends? Why?

A: Let G be a graph with 4 vertices, one vertex representing each person in the group. Join two…

Q: Three different classes contain 20, 18, and 25 students, respectively, and no student is a member of…

A:

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: 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…

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.