Martha invited 4 friends to go with her to the movies. There are 120 different ways in which they can sit together in a row of 5 seats, one person per seat. In how many of those ways is Martha sitting in the middle seat?

Q: There are 12 people in a dinner gathering. In how many ways can they arrange themselves around a…

A: We use permutations and combinations. Number of ways to arrange n objects in n places is n! Number…

Q: A street vendor sells six different kinds of fresh fruit: apples, bananas, oranges, pears, kiwis and…

A: Given that , a street vendor sells six different kinds of fresh fruits each worth $1. To find the…

Q: There are 22 students in a fraternity. In how many ways can a committee of 6 students be selected?…

A: Given that Number of students=22 Number of students selected=6

Q: There are 4 oranges, 5 apples and 6 mangoes in a basket. In how many ways can a person make a…

A:

Q: How many ways are there for 6 people sitting around a circular table to pick from 12 entrees so that…

A:

Q: A dress-shop owner has 8 new dresses that she wants to display in the window. If the display window…

A: A dress-shop owner has 8 new dresses.  She wants to display in a window which has 5 mannequins.  So…

Q: A scholar is choosing six books to take on vacation from a stack of 34. A. How many different…

A: Solution

Q: Apple decided to give an apple watch to the first person in line, an iPhone to the second person in…

A: From the given information, Apple decided to give apple product to all three persons who stand up in…

Q: How many ways are there to pick three dipping sauces, if you can pick three of the same?

A:

Q: A teacher wants to assign 4 different tasks to her 4 students. In how many possible ways can she do…

A: Solution

Q: A typist has 5 letters and 5 addressed envelopes. In how many different ways can the letters be…

A:

Q: How many ways can an adviser choose 4 students from a class of 12 if they are all assigned the same…

A: We have to find the number of ways that can an adviser choose 4 students from a class of 12 if they…

Q: In a school of 200 students, a math team, consisting of 15 students, is to be formed. Two team…

A:

Q: The University of Montana ski team has fifteen entrants in a men's downhill ski event. The coach…

A: In theory of combinatorics, the way of selecting r objects from n objects with regard to the order…

Q: In the local boating pond there are 11 plain wooden boats, each with a different number. The owner…

A:

Q: In a bag containing 5 white balls and 6 black balls, how many ways can we draw a white or a black…

A:

Q: A young boy asked his mother to get 6 game cartridges from his selection of 11 arcade and 7 sport…

A: Given: Number of arcade =11 Number of sports game =7

Q: Ms. Goodman has 18 students in her first-grade class. In how many ways can 4 students be picked to…

A: We will use combination metod for solving this question.

Q: There are 18 males and 14 females in a classroom. A president, secretary and vice- president must be…

A: There are 18 males and 14 females in a classroom. A president, secretary and vice president must be…

Q: 5 Brady went to a big parade and saw 42 different marching bands. If each band had an average of(120…

A: Brady went to a big parade and saw 12 different marching bands. Each band had an average of 120…

Q: At Rosemont High School, 14 players are on the varsity bas- ketball team, 35 players are on the…

A: Given: Let A denotes the varsity basketball team and B denotes the varsity football team then,…

Q: Mary wants to organize a party with only 10 people. In how many ways can she choose those 10 people…

A:

Q: The university of Montana ski team has 8 entrants in a men’s downhill ski event. The coach would…

A: Permutations: The number of permutations of r items selected from n items is, Prn=n!n-r! The…

Q: Three married couples have bought 6 seats in a row for a concert. In how many ways can they be…

A: The number of arrangement in a row is n!.

Q: 2. Dylan, Andrew, Hailey, and Jordan ran in a race of 25 people. In how many different orders can…

A:

Q: There are 9 female board members and 21 male board members. How many ways are there to make a…

A: We use combination to find number of way to make a committee.

Q: Pat has 9 flowerpots, and she wants to plant a different type of flower in each one. There are 11…

A: We have given that - Pat has 9 flowerpots. In garden shop there are 11 types of flower available. We…

Q: The president has a team of 20 trusted bodyguards. In how many ways can the president choose 5…

A: Given,  The president has a team of 20 trusted bodyguards  We have to find the number of ways of…

Q: A fan of country music plans to make a custom CD with 12 of her 25 favorite songs. How many…

A: Given dataTotal songs N = 25 No of combinations for size 12 is given by

Q: The math club needs to send 4 representatives – 2 females and 2 males to a meeting. If there are 12…

A: GivenNo. of female math club members = 12No.of male math  club memebrs = 23no.of representatives  to…

Q: How many different ways are there for the 10 people to stand in line to buy movie tickets?

A: How many different ways are there for the 10 people to stand in line to buy movie tickets?

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: In a music club with 15 members, 7 people played the piano, 11 people played the guitar, and 2…

A: Given that in a music club of 15 members 7 people played the piano, 11 people played the guitar and…

Q: Erin invited three couples to watch a theater musical sponsored by my husband. If the 6 VIP seats…

A: There are total three couples.

Q: There are 10 books in the box, 4 of them are art books. a) In how many ways can you select 5 books…

A: Concept:

Q: There are 3 apples, 5 pears and 4 oranges in a basket. If a waiter were to line up these fruits side…

A: There are 3 apples, 5 pears and 4 oranges in a basket. Total fruits = 3+5+4 = 12 n distinct objects…

Q: There are 5 different types of fruits and n different types of vegetables in a grocery shop. If…

A: Hey there! Thank you for posting the question. Since there are multiple questions posted, we will…

Q: A restaurant offers 8 entrees and 9 desserts. In how many ways can a person order a two-course meal?

A: We can find the answer as below.

Q: How many ways are there in choosing 3 books from a shelf of ( 83 ) books ?

A: The number of way for choosing 3 books from a shelf of 83 books is C383 =83!3!×(83-3)!…

Q: There are 7 boys and 3 girls in a class. How many different ways can the classroom teacher create a…

A: From the given information,   Number of boys = 7 Number of girls = 3   Total = 10

Q: There is a town party in Pleasantville where 6 families of 3 people each get together. If one…

A:

Q: in a row on his bedroom wall, but only has space for 5 of them. If his favourite poster must go in…

A: In how many ways can Liam put the posters up :

Q: There are 4 seats in a cinema hall. In how many ways can 4 people sit in a cinema if only 2 of them…

A: 6 ways

Q: Bruce has 5 different jackets, 3 pairs of jeans, and 8 pairs of shoes. In how many ways can he…

A:

Q: he BMCC web-design club has 40 members. a. In how many different ways can it select a group of 4…

A: Given Data: The number of members in the web-design club is: n=40 The number of members to be…

Q: From among 5 engineers and 7 technicians, it is required to form a committee consisting of 2…

A:

Q: A club with 25 members is to select five officers (president, vice president, secretary, treasurer,…

A:

Q: You baked seven cupcakes of different flavor. In how many ways can you  give two cupcakes each to…

A: Here Given  Total No of cupcakes=7 No of given to each friends=2 No of cupcakes keep with himself=1

Q: How many ways are there to select 2 people from a group of 7 to serve on a committee? What kind of…

A: We have given there is group of 7 and we have to select 2 people from this group to serve on a…

Q: 2. The view of Sampaloc Lake is a very nice background to take pictures of. How many ways can 5…

A: Find the number of ways of arrangement

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.