If there are 3 representatives from Company A and 4 representatives from Company B meet. If they shake hands with everyone from a different company. How many handshakes occurred?

Q: At the end of the day, a bakery gives everything thatis unsold to food banks for the needy. If it…

A: Consider, Number of apple pies left (n) = 12 Number of food banks (r) = 6

Q: An insurance agent has a list of 7 prospects and decides to telephone 5 of the prospects today and…

A: we want to find different ways can the agent telephone the prospects

Q: In how many ways can a commitee of 9 students be chosen from 8 juniors and 10 seniors if there must…

A: Given data: 8 juniors and 10 seniors

Q: How many ways can 6 boys stand in a line if a certain boy must come first?

A:

Q: Out of a list of 20 colleges, how many ways to schedule the visit of 10 of them (one for each month…

A: Given Information: Total number of colleges = 20 Number of college should visit =10 Number of…

Q: There are 8 people in a room. Each person shakes hands with each of the other people once and only…

A: Given, There are 8 people in a room. Each person shakes hands with each of the other people once and…

Q: In how many ways can you arrange five books along a shelf, assuming that the order of the books…

A: Given  arrange five books

Q: There are 10 students in a class. In how many ways can an instructor give at most three students a…

A: n = 10 Let x represent the number of students given grade A.   The number of ways a student can be…

Q: In how many ways can 9 individuals be seated in a row of 9 chairs if two individuals wanted to be…

A: Permutation is the method that used to measure the number of arrangement in the data set. In this…

Q: How many ways that two girls and 4 boys can fall in a line of there must be a girl and a boy in the…

A: Let us assume there are three persons A, B and C sitting beside each other. The different ways in…

Q: how many different ways can a coach choose three players from 8 bench players to replace 3 of the 5…

A: He can select 3 of the 5 starting players in 5C3=10 ways. He can select 3 of the 8 bench players in…

Q: In a friend group of six, how many ways can we arrange them in a line for a photograph?

A: In a friend group of six, we have to arrange them in a line for a photograph.

Q: With 20 people seated around a tabke, how many ways can 3 people be selected without any being…

A: It is given that there are 20 people seated around a table. The total number of ways of selecting 3…

Q: Suppose you host a party for 19 of your close friends. In total, there are 20 people at the party.…

A:

Q: There are 6 women and 9 men signed up to join a swing dance class. In how many ways can the…

A: Given Information: There are 6 women and 9 men signed up to join a swing dance class. We are asked…

Q: If the 50 guests in the party described in question number 5 where actually couples (so there are 25…

A: Total guest , n = 50 Total Number of Handshakes  = n×(n-1)2=50×492=1225

Q: If 3 representatives from Company A, 4 representatives from Company and 2 lawyers (from a different…

A: Given data , 3 representatives from Company A , 4 representatives from Company B , 2 lawyers from (…

Q: How many license plates can be made using two letters followed by four digits (0-9), allowing…

A: From this given information, license plates can be made using two letters followed by four digits…

Q: Of 20 possible​ books, you plan to take 3 with you on vacation. How many different collections of…

A:

Q: A parent brings 4 children to a movie and the family sits in a row of 5 seats. How many ways can…

A: There are total 5 members to sit. 4 of them are children and one parent. The parent sit on one one.…

Q: How many outfits can be constructed with 1 shirt, 1 pants, and 1 tie from a wardrobe of 2 shirts, 5…

A: The given problem is based on combination {Because order doesn't matter}. The combination of…

Q: A person has 8 friends, of whom 5 will be invited to a party.How many choices are there if 2 of the…

A: Combination Rule:The arrangement of r objects from n different objects is given by:

Q: How many ways are there to pair 2n people?

A: We need to compute the number of ways in which 2n people can be paired.

Q: A woman has 11 close friends. In how many ways can she invite 5 of them to dinner if two of them are…

A: Given, A woman has 11 close friends. To find,  How many ways can she invite 5 of them to dinner if…

Q: There are 10 students in a class. In how many ways can an instructor give at least one student a…

A: There are 10 students So sample size, n= 10 And we've to find ways for at least 1 student. So r= 1

Q: Suppose you have 11 books and you randomly pick 4 to take on vacation with you. How many ways can…

A:

Q: Suppose a club has 20 members. a. How many ways can they select a chairperson to lead a small…

A: Since you have asked a question with multiple parts in a single request, we would be answering only…

Q: There are 10 people in a meeting. In how many ways can you arrange your participants around a ROUND…

A: Total ways in which 10 people be arranged around a round table so that 4 people sit beside each…

Q: Each marble bag sold by Deshaun's Marble Company contains 5 orange marbles for every 6 green…

A:

Q: If 5 students are to be seated in 5 chairs, how many ways can they be seated in a circle?

A: Let, n be the number(n)=5 The total number of arrangement = 1 x (n-1)!…

Q: If 10 people come from different places and shake hands in how many different way could this be done

A: The formula for the number of handshakes possible with n people is          handshakes = n*(n -…

Q: If four students out of 35 students in a classroom are chosen to have lunch with the principal how…

A: If four students out of 35 students in a classroom are chosen to have lunch with the principal how…

Q: There are 15 persons in a party and if each 2 of them shakes hands with each other, how many ways…

A: Given data: 15 persons in a party Each 2 of them shakes hands with each other

Q: In a group of students, 100 students know Hindi, 50 know English and 25 know both. Each of the…

A:

Q: If a guy has 4 apples and he gives away the 3 how many apples will he have ?

A:

Q: How many ways can 7 people fall in line if 2 persons doesn’t want to be seated next to each other?

A:

Q: If 5 horses are in a race and they all finish with no ties, in how many ways can the horses finish…

A: Given information- We have given that 5 horses are in a race. They all finish the race with no ties.…

Q: A girl is allowed to pick 5 out of 18 children’s books to take home from the library. In how many…

A: Solution: 1. From the given information, a group of 5 books are to be chosen from 18 children’s…

Q: If 72 students which represent 2/3 of the class participated in the Alay Lakad, how many students…

A:

Q: The president of the college asked a fraternity to submit a list of 7 students to serve as guides at…

A:

Q: A business has 26 applicants for a job. How many ways can they pick 7 of the applicants to…

A: A business has 26 applicants for a job. To find how many ways can they pick 7 of the applicants to…

Q: What if the jelly bean machine gives 9 jelly beans to the first customer who put in a coin, 13 to…

A: If the initial term of an arithmetic progression is {\displaystyle a_{1}} and the common difference…

Q: Assume that five men and five women are to sit in a row of ten chairs how many ways can these people…

A: Five men and five women are sitting in a row of ten chairs.

Q: Suppose that you must choose three people to meet with a customer. You have nine people to choose…

A: Given data, Total number of people (n)=9 Number of people to meet with a customer (r)=3

Q: Suppose you are asked to choose three movies. If there are 20 different movies, in how many ways can…

A: According to the combination rule, if r distinct items are to be chosen from n items without…

Q: There are 12 teams in a league. In how many ways can the teams finish first, second, third, and…

A: A permutation is a mathematical tool that helps us to find the number of possible arrangements in a…

Q: there are 4 men and 5 women to form a meeting of a man and a women, in how many ways can a committee…

A: Given,no.of men=4no.of women=5

Q: A teacher will randomly award three students with extra credit. How many possible ways can the…

A: Given that  , a teacher will randomly award three students with extra credit .  Teacher can pick…

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 committee of six is to be made from 4 students and 8 teachers. In how many ways can this be done:…

A: Given that  A committee of six is to be made from 4 students and 8 teachers.  To find the In how…