At Mr. Furry's Dance Studio, every man must dance the last dance. If there are six men and nine women, in how many ways can mixed gender couples be formed for the last dance?

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

A:

Q: From a group of 7 women and 8 men a committee consisting of 4 men and 3 women is to be formed. How…

A: Given, 7 women and 8 men committee size 4 men and 3 women

Q: If women represent 53% of a town, and there are 9,805 women in the town, how many people are in the…

A: Let there are total X people in the town.

Q: At a dance, there are 20 girls and 20 boys. How many ways are there to form 20 pairs? How many if…

A: We have to use combinations to answer this problem.

Q: In an art gallery there are 10 paintings to be hung on a wall, but 5 of which must be hung in a row.…

A: There are 10 paintings in an art gallery. Of which 5 paintings must be hung in a row.

Q: There are 16 seniors and 20 juniors in a particular social organization. In how many ways can 2…

A:

Q: How many ways can a class president, vice-president, and secretary be selected from each of the…

A: Given data:   The total number of members in the seventh grade is N=110. The total number of members…

Q: A small high school has 30 seniors, 20 juniors, and 10 sophomores. If 3 students are chosen from…

A: A small high school has 30 seniors, 20 juniors, and 10 sophomores. If 3 students are chosen from…

Q: There are three boys and three girls at a party. In how many ways can they be seated if they can sit…

A: Given, There are three boys and three girls at a party they can sit down three at a time

Q: You have 3 science books, 2 language books, and 4 philosophy books. In how many ways can they be…

A:

Q: At Wingstop, customers ordering a family meal can choose 4 different wing flavors. If Wingstop has…

A: Given problem is : At Wingstop, customers ordering a family meal can choose 4 different wing…

Q: Student Painters, which specializes in painting the exterior of residential buildings, has nine…

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

Q: There are 280 students in 20 classes. If the number of students in each class is  the same, then how…

A: We have no of students..

Q: When an ice cream shop was founded, it made 37 different flavors of ice cream. If you had a choice…

A: Given- When an ice cream shop was founded, it made 37 different flavors of ice cream. If we had a…

Q: At a dinner party, 6 men and 6 women sit in a round table. In how many ways can they sit if Bob,…

A: Number of ways to arrange N person around the round table is (N-1)!. Here, there are 6 men and 6…

Q: a candle company sells individual candles, boxes with 8 candles, or containers with 15 boxes. At the…

A: Given:The number of candles in a box is 8.The number of box in a container is 15.At the beginning,…

Q: A take-out restaurant offers 6 different kinds of sushi. If they have exactly 4 pieces of eachkind…

A: Given: There are 6 different kinds of sushi, with exacctly 4 pieces of eachkind. To determine:…

Q: A man owns 8 pairs of pants, 15 shirts, 12 ties, and 3 jackets. How many different outfits can he…

A: Given he has 8 pairs of pants, 15 shirts, 12 ties, and 3 jackets

Q: how many ways can each person select one fairy form her own basket?

A: Amy, Betsy, and Cindy are each given a fruit basket. Each basket contains one apple, one pear, one…

Q: At Mr. Furry's Dance Studio, every man must dance the last dance. If there are five men and seven…

A: The formula for Permutation is nPr = n!/(n – r)!. Explanation: Consider that r items need to be…

Q: A boy owns 7 pairs of pants, 2 shirts, 20 ties, and 7 jackets.  How many different outfits can he…

A:

Q: 30% of Grandpa Neil's stamps have images of flags on them. If he has 75 flag stamps, how many stamps…

A: In question, Given that 30% of Grandpa Neil's stamps have images of flags on them. If he has 75 flag…

Q: At a local pizza shop, they are running a "5 topping special." In have many ways can 5 pizza…

A: Given: Number of available toppings, n=14 The objective is to find the number of ways in selecting 5…

Q: 5. Rowena would like to invite 7 friends to go on a trip but has room for only 4 of them. In how…

A: Combination:   It is nothing but the selection of objects where the order of selection is not…

Q: A man owns 6 pairs of pants, 7 shirts, 8 ties, and 2 jackets. How many different outfits can he wear…

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: The 50 members of a club include both the club president and the club treasurer. All 50 members want…

A: Topic- permutations and  combinations

Q: 3. Anabelle would like to invite 9 friends to go on a trip but has room for only 5 of them. In how…

A: Question: Anabelle would like to invite 9 friends to go a trip but has room for only 5 of them . In…

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 box of Mrs. Donuts contains 8 honey dipped, 6 bavarians, and 7 chocolate filled donuts. How many…

A: Given,no.of donuts honey dipped=8no.of bavarians donuts=6no.of chocolate donuts=7

Q: To fill a number of vacancies, the personnel manager of a company has to choose three secretaries…

A: The number of ways a company has to choose three secretaries from among ten applicants can be done…

Q: 2) Abby is adopting kittens from the pet store. If there are 18 kittens, how many ways can she…

A: In this question we have to find in how many Abby choose two kittens if there are two kitten .

Q: A restaurant has on its menu four fish dishes, two potato dishes, and two green vegetables. In how…

A: Giventhe total number of fish dishes = 4the total number of potato dishes = 2the total number of…

Q: A group of 12 service dogs have been trained as K-9 units to assist the SWAT unit. How many ways are…

A: This is a combinatorics problem. So number of ways to select 3 dogs from 12 is:  C12,3=12!3!12-3!…

Q: (a) If first prize is $100, second prize is $80, and third prize is $30, in how many different ways…

A: Given: People buy raffle tickets = 200

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

A:

Q: A committee of 6 people, with two of the six to be designated chair and vice-chair, is to be…

A: A committee of 6 people, with two of the six to be designated chair and vice-chair, is to be…

Q: An ice cream parlor has 28 different flavors, 8 different kinds of sauce, and 12 toppings. a. In how…

A: Given that, An ice cream parlor has 28 different flavors, 8 different kinds of sauce, and12…

Q: 3. Marty is a bookworm and he has various collections of novels, series and other story books. If he…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: A class of 15 students needs to elect a class president, vice president, treasurer, and secretary.…

A: Consider the given information. The class have 15 student and there are four position as given in…

Q: A disc jockey (DJ) has 11 songs to play. Five are slow songs, and 6 are fast songs. Each song is to…

A:

Q: _6. Rylan's basketball team has 11 players. How many ways can his coach choose five starting…

A: Given;  1): No of player =11  To choose 5  starting players from the 11 players then nonof ways ?…

Q: there are 18 people from the mathematics department and 325 people from the computer science…

A: see my solution below

Q: You and 3 friends are moving into a 4-bedroom house and need to decide who gets which room. How many…

A: There is total 4 persons.

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: In how many ways can Mrs. Smith give a chocolate bar, a bag of potato chips, and a can of cane juice…

A: Mrs. Smith give a chocolate bar , a bag of potato chips and can of cane juice to 3 of the 21…

Q: How many ways are there to stack an​ ice-cream cone with 4 scoops if the choices are   a.…

A: For flavours must be different then once used flavour can't be used next time. So in first stack we…

Q: There are 12 seniors and 8 juniors in the Mercy College Chess Club. In how many ways can a team…

A: From the given information,   There are 12 seniors and 8 juniors in the Mercy College Chess Club.…

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.