Suppose there are 21 different competitors at a barbeque competition. Judges are going to award 5 places. How many different ways can the competition finish?

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: In how many ways can 4 pizza toppings be chosen from 12 available toppings? Your answer is:

A:

Q: How many different ways can a theatrical group select 2 musicals and 3 dramas from 11 musicals and 8…

A: Given,no.of musicals=11no.of dramas=8

Q: You must select 3 individuals from a group of 5 for a conference. How many teams of 3 might you…

A:

Q: A clothing store has a selection of 80 different ties. How many ways can six ties be selected for…

A: It is given that, A clothing store has a selection of 80 different ties. Chris and Alex select 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 coach had 21 people try out for the team, but only 13 people can make the team. How many different…

A:

Q: How many ways can 10 people line up at the front of a class if Billy and Samantha are together?

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: How many ways can a committee of four people be chosen from a group of eight people?

A: Given data, Total number of people = 8 People select for committee = 4

Q: in a qualifying race for a road cycling event, 15 men competed for five slots.How many different…

A: Given The total number of men (competed)=15 The number of slots=5 Apply permutation formula…

Q: A photographer is asked to submit 7 photos from a collection of 14. How many ways can the photos be…

A:

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: A New club at Arvin High has 22 members. In how many ways can the club elect a president and Vice…

A: The number of members in the club is 22. The number of ways of electing a president is C122=22.…

Q: How many ways can 7 people line up in a cafeteria line? How many ways can five people be chosen from…

A:

Q: A musician plans to perform 9 selections. In how many ways can she arrange the musical selections?

A: Given A musician plans to perform 9 selections

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 a ballroom dance lesson, the instructor chooses 3 men and 3 women to demonstrate a new pattern.…

A: There are 9 women and 7 men in the class, the instructor chooses 3 men and 3 women to demonstrate a…

Q: How many different ways can 12 skiers in the Olympic finals finish the competition?

A: Solution: Consider the given 12 skiers in the Olympic final The total number of different ways to…

Q: How many different committees of 3 people can be chosen from a group of 8 people?

A: Total number of people in the group are 8. Total number of people for the committee is 3.

Q: How many ways can seven people line up at a ticket window?

A: There are 7 people. n=7

Q: There are 34 students in a high school senior class. In how many ways could the yearbook choose the…

A:

Q: How many ways can 4 officers be elected from 12 candidates?

A: From the provided information, There are 12 candidates from which 4 officers will be elected.

Q: If 20 women are entered in the Miss Georgia contest, in how many different ways can the judges…

A: Given that 20 women are entered in the Miss Georgia contest.

Q: From a group of 36 people, a jury of 12 is selected. In how many different ways can a jury of 12…

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

Q: how many different ways can 15 runners finish in the first five places of a race?

A: It is given that n is 15 and r is 5.

Q: How many ways can you choose seven people from a group of twenty?

A: Solution: Combinations: Suppose there are n objects and r objects to be chosen. Then, combination…

Q: In a club consisting of 15 members, how many different ways can a 4-person committee where everyone…

A: It is given that the club contains 15 members.

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

A:

Q: A college golf team consists of four players who are ranked from 1 through 4. If a golf coach has…

A: Given that a college golf team consists of four players who are ranked from 1 through 4.

Q: As a television executive, you have been given 24 shows to choose from to run during your prime time…

A:

Q: The All-County Goat Show will award the blue ribbon for 1st place, red ribbon for 2nd place, and…

A: Using permutations and combination

Q: In how many ways can you arrange 4 people to be seated in a round table?

A:

Q: 2. Your friend Carlos brought over 10 videos. Together, you choose 4 of them to watch. How many…

A:

Q: The Grossmont College Student Council has 12 members.  How many different groups can be formed to…

A:

Q: How many ways can you select 3 students from a class of 30 students to serve as representatives for…

A: Follow the procedure given below.

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: How many ways can seven people be seated at a roundtable relative to the door of a room?

A: Number of people are = 7 The number of permutation of n elements in a circle is: P=n-1!

Q: From a club of 24 members, a President, Vice President, Secretary, Treasurer and…

A: Given Data: The number of members in the club is: n=24 Five members such as a president, vice…

Q: What are all the ways in which the top 4 racers in a 20 person race can finish?

A: Introduction:In the given situation, the number of persons participated in the race is 20. The…

Q: If 20 paintings are entered in an art exhibit, in how many different ways can the judges award a…

A: It is given that, 20 paintings are entered in an art exhibit. Then judge award the first prize to…

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: As a television executive, you have been given 22 shows to choose from to run during your prime time…

A: Total number of shows Available n = 22 Total shows to be selected r = 12

Q: A doctor visits her patients during morning rounds. In how many ways can the doctor visit 8 patients…

A: The number of ways that the doctor can visit 8 patients during the morning rounds is,The number of…

Q: As a television executive, you have been given 19 shows to choose from to run during your prime time…

A:

Q: 14 people try out for a basketball team, how many different ways are there to select 5 players if…

A: Given information: Total number of people who try out for a basketball team(n)=14. Number of…

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

A:

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: A book club offers a choice of 5 novels from a list of 10. How many 5-novel selections can be made?

A: Given data: The total numbers of books are n=10. The numbers of novels selected are x=5.

Q: How many committees could be formed from 10 students if: a) there must be at least 8 people? b)…

A: Introduction: The number of different ways in which r different objects can be selected out of n…

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.