There are 6 men and 8 women auditioning to be in the school play. Answer the following questions: 1. If the cast consists of 2 women and 2 men, how many different casts can be selected? 2. If the cast consists of 2 women or 2 men, how many different casts can be selected?

Q: Suppose there are 21 different competitors at a barbeque competition. Judges are going to award 5…

A: Given: 21 different competitors The total award is given = 5

Q: A casting director wishes to find one cat and one dog to cast in his play. If he plans to audition 5…

A: The objective of this question is to find the number of different ways the casting director can…

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

A:

Q: A car manufacturer allows you to customize and order vehicles on their website. When customizing…

A: Given: There are 2 different sizes of the engine, 2 different types of transmission, 8 different…

Q: A basketball team contains 21 players. If 5 people can be on the court at one time, how many…

A: Given that Number of players (n)=21  Number of people on the court at one time  r=5  We have to find…

Q: There are 15 boys and 12 girls that try out for a chorus. The choir director will select 10 girls…

A:

Q: A ice cream store offers 7 ice cream flavors and 12 toppings. If you want to eat 3 different ice…

A:

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: A company has 42 employees. How many different ways can 7 people be chosen to serve on a committee…

A: We can choose the 7 persons in 42C7 ways  Where 7 people are chosen then there are (42-7)=35 people…

Q: The group of qualified candidates for five positions is made up of eight women and six men. How many…

A:

Q: There are 29 students in a homeroom. How many different ways can they be chosen to be elected…

A: Given,Total no.of students=29

Q: How many different committees can be formed from 12 teachers and 39 students if the committee…

A: No. of teachers=12no. of students=39committee should consist of 3 teaches and 2 students

Q: a law firm has 8 male and 6 females lwayers. a committee of 5, two male lawyers and 3 female…

A: The objective of this question is to find out the number of possible committees that can be formed…

Q: A department consists of 5 men and 7 women. From this department you select a committee with 3 men…

A: From the provided information, A department consists of 5 men and 7 women. We select a committee…

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: From the 9 male and 6 female sales representatives for an insurance​ company, a team of 4 men and 3…

A:

Q: The Cincinnati Angry Unicorns is a local swimming team which currently has seventeen members. If…

A:

Q: A four-person committee is to be selected from an organization’s membership of 12 people.  How many…

A:

Q: In a large family, 20 have parrots, 15 have rabbits, and 5 have both. One own a pet dog. How many…

A: In a large family, 20 have parrots, 15 have rabbits, and 5 have both. One own a pet dog. We need to…

Q: Jana has 10 blouses, 5 pairs of shoes, 5 skirts,and 5 hats. How many distinct 'outfits' does she…

A: No.of blouses=10 no.of pairs of shoes=5 no.of skirts=5 no.of hats=5

Q: After the tryouts for the volleyball team, the coach selects 14 people to join the team. Due to a…

A: To determine the number of ways the coach can choose 7 people out of 14, we use the combinations…

Q: A class of 15 students will chose between style of course text book; one text for each student. The…

A:

Q: Suppose you have a choice of ten TV sets that can be matched with any of six DVR players and eight…

A: Multiplication rule of counting: If a task consists of a sequence of choices in which there are ‘a’…

Q: A large research project is looking for more researchers. There are 8 spots open on the research…

A:

Q: From 5 men and 4 women, how many committees can be selected consisting of: - 3 men and 2 women? - 5…

A: Solution: Given information: 5 men  4 women.   3 men can be selected from 5 men in 5C3 ways.  and 2…

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

A:

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.