A sales assistant is hanging 13 sweaters on a rack. He has 3 brown sweaters, 4 purple sweaters, and 6 pink sweaters. In how many distinct orders can the sweaters be arranged if two sweaters of the same color are considered identical (not distinct)?

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

A: Solution

Q: A sales assistant is hanging 12 sweaters on a rack. He has 3 gray sweaters, 4 brown sweaters, and 5…

A: 3 - grey 4 - brown 5 - black  ... 12 total

Q: Elsa is putting 12 colored light bulbs into a string of lights. There are 3 green light bulbs, 6…

A: Given that     Total number of light bulbs present = 12                                Number  of…

Q: How many different ways can 3 outfielders and 4 infielders be chosen from 9 outfielders and 7…

A: Given: How many different ways can 3 outfielders and 4 infielders be chosen from 9 outfielders and 7…

Q: Six people are about to enter a cave in a single row. In how many ways could the arrange themselves…

A: Given: Six people are about to enter a cave in a single row

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

A:

Q: From a club of 17 people, in how many ways can a group of six members be selected to attend a…

A:

Q: There are 18 mathematics majors and 325 computer science majors at a college. In how many ways can…

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

Q: A pianist plans to play 9 pieces at a recital. In how many ways can she arrange these pieces in the…

A:

Q: A fast food restaurant advertises that it offers any combination of 8 condiments on a hamburger,…

A: The number is obtained as follows: The number of choosing none of the condiments on a hamburger:…

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

A:

Q: How many different committees consisting of 3 men and 2 Jadies each can be for 3. from a group of 6…

A: Hi! Thank you for the question As per the honor code, We’ll answer the first question since the…

Q: A buyer of a new sedan can custom order the car by choosing from 5 different exterior colors, 3…

A:

Q: How many different ways can the golf pro at a golf club select a foursome consisting of 1 man and 3…

A: Given,   Number of males = 8 Number of females = 11   The objective is to find how many different…

Q: A sales assistant is hanging 11 sweaters on a rack. He has 3 brown sweaters, 2 gray sweaters, and 6…

A: From the provided information Total sweaters = 11 Brown sweaters = 3 Gray sweaters = 2 Green…

Q: If 11 people are to be seated in a row of 11 chairs, how many different seating arrangements are…

A: Given: 11 people are to be seated in a row of 11 chairs. The objective is to find different seating…

Q: A sales assistant is hanging 11 sweaters on a rack. He has 5 white sweaters, 4 brown sweaters, and 2…

A:

Q: In how many ways can 9 books be arranged on a shelf if 5 particular books must always stand…

A:

Q: How many ways can a baseball coach arrange the order of 9 batters if there are 13 players in the…

A:

Q: From a club of 16 people, in how many ways can a group of five members be selected to attend a…

A: Given Data: The number of people in the club is: n=16 The number of members required is: x=5 The…

Q: An equestrian club has seven members. If the club wants to select a president, vice president, and…

A:

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: 24. Box A contains 7 balls and box B contains 16 balls. How many different selections of 10 balls…

A: Determine the different selections of 10 balls that can be made. The different selections of 10…

Q: A computer user has downloaded 15 songs using an online file-sharing program and wants to create a…

A: Given that the computer use has downloaded 15 songs using an online file-sharing program and wants…

Q: How many ways can 2 students be selected from a group of 5 students if order does not matter?

A: Given information- We have given that we have given a group of 5 students. We have to select 2…

Q: In how many distinct orders can the sweaters be arranged if two sweaters of the same color are…

A: HERE GIVEN , A sales assistant is hanging 11 sweaters on a rack. He has 5 green sweaters, 3 pink…

Q: How many different sets of 6 cards each can be formed from a standard deck of 52 cards?

A: Please find attachment for the details solution

Q: How many different arrangements can be made using all the letters in CALGARY, if the first letter…

A: CALGARY If the first letter must be G.  Then, Starting with G, need to arrange the remaining 6…

Q: How many formations of committee from 10 persons are possible if the committee consists of one…

A: In this question, the concept of Permutation and Combination is applied. Permutation  Permutations…

Q: a restauranr offers 4 different flavors of coffee,3 different soup selections and 4 different…

A:

Q: In a​ bag, there are 6 purple and 12 green marbles. If you reach in and randomly choose 5 ​marbles,…

A: Given, there are 6 purple and 12 green marbles in a bag To find the number of ways to choose exactly…

Q: A sales assistant is hanging 12 sweaters on a rack. He has 3 pink sweaters, 4 white sweaters, and 5…

A:

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

A: 2. There are 4 people Dylan,Andrew,Hailey and Jordan Here The places are also 4 The race are start…

Q: John is arranging 11 cans of food in a row on a shelf. He has 5 cans of beans, 5 cans of olives, and…

A: Fundamental method of counting is used here.

Q: Agustina owns all five books in the Spiderwick Chronicles series. In how many different orders can…

A: Given: Number of books = 5

Q: Troy is putting 13 colored light bulbs into a string of lights. There are three white light bulbs,…

A:

Q: A computer user has downloaded 15 songs using an online file sharing program and wants to create a…

A: Given data: Total songs  = 15  13 =  songs to use in his portable CD player  To find: How many…

Q: you have 11 tubs of paint how many distinct color groupings can you make with your paint?

A: Total given colors are   11 Total distinct colors grouping   ?   we can solve this question with the…

Q: Find the number of ways in which 6 teachers can be assigned to 4 sections of a math course if no…

A: Solution: 5. From the given information, there are 6 teachers and 4 sections.

Q: A group of 8 people, including Betty and Bob, are going to take a group photo. In how many ways can…

A: Number of people in group is 8 .

Q: A teacher and his eleven students are standing in a single file line waiting to enter the cafeteria…

A: We have given that a teacher and his eleven students are standing in a single file line waiting to…

Q: A sales assistant is hanging 11 sweaters on a rack. He has 5 black sweaters, 4 green sweaters, and 2…

A: Given dataTotal sweaters = 11Black sweaters = 5Green Sweaters = 4White sweaters = 2Total…

Q: Mai is arranging 12 cans of food in a row on a shelf. She has 8 cans of beets, 3 cans of beans, and…

A: There are total 12 cans of food, among which 8 cans are beets, 3 cans are beans and 1 can is olives.

Q: A contractor has three styles of homes, each with three styles of garages, two styles of decks, and…

A: Answer: First we need to list all the possible selections and the number of choices that each…

Q: A bus has 8 vacant seats in the first rows. If 3 additional passengers enter the bus, in how many…

A: For the number of ways of their seating, we need to use combination.

Q: Two freshmen and three sophomores from a sorority will attend a conference. If the sorority has 12…

A:

Q: In how many ways can a teacher arrange 6 students in the front row of a classroom with a total of 20…

A:

Q: in how many ways can three classmates oliean, kagan, kelvin , and jet arrange themselves seated in a…

A: To find in how many ways can three classmates oliean, kagan, kelvin , and jet arrange themselves…

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.