4. How many ways we can choose champion, first runner -up and 2 runner-up out of 20 participants?

Q: 1.) How many ways may 4 cards be drawn randomly from a deck of 52 cards? 2.) How many ways may 5…

A: Solution-: We find, (1) How many ways may 4 cards be drawn randomly from a deck of 52 cards? (2) How…

Q: How many ways can 6 boys stand in a line if a certain boy must come first?

A:

Q: 1. In how many ways can the 10 candidates in the Ms. Universe win the Ms. Universe title, First…

A:

Q: 5. Suppose six pairs of similar-looking boots are thrown together in a pile. How many individual…

A: Let us assume there are three persons A, B and C sitting beside each other. The different ways in…

Q: 10. A tourist group visiting Las Vegas for 5 days would like to stay in 5 different hotels. If the…

A: There are 10 hotels and the people are staying for 5 days so the choice needs to be made of 5 hotels…

Q: 2. A clothing store wants to stock sweatshirts that come in four sizes (small, medium, large,…

A:

Q: 2. Ten students are in a race. First, second, and third places will win medals. In how many ways can…

A:

Q: How many ways may 5 students be elected from a club with 45 members?

A: Total number of students = 45 Number of students to be selected = 5

Q: 11. In how many ways can 4 boys and 5 girls sit in a row if the boys and girls must alternate?

A: Disclaimer: Since you have asked multiple questions, we will solve the first question (i.e. #11) for…

Q: How many ways are there to choose first, second, and third prizes in an art contest with 18 entries?

A: Introduction:According to the permutation rule, if r distinct items are to be chosen from n items…

Q: In how many ways can a comittee of 6 be chosen from 6 administrators and 4 supervisors if all are…

A:

Q: 2. In how many different ways can they arrange to give everybody a chance to experience the ride?

A: Number of people=7, number of bike available=4. To find the number of ways of arrangements so that…

Q: 4. What is the number of different ways to divide a group of 20 people equally into 2 sub-groups?

A: Permutation and combinations

Q: How many different ways can 5 out of 8 different shirts, 4 out of 10 different pieces of slacks, and…

A: Different ways can  5 out of 8 different shirts, 4 out of 10 different pieces of slacks, and 3 out…

Q: A coin is tossed five times. In how many ways can it fall three heads and two tails?

A:

Q: 4. Your school is hosting a Mathletes competition in which senior and junior teams will be entering.…

A: Selection of x items from n objects can be represented by combination  Cxn and arrangement of same…

Q: In how many ways can an HR department head choose one or more applicants from six eligible…

A: Number of eligible applicants=6Choose one or more applicants Let, Number of ways=n=?

Q: A automobile race contains 15 racecars. In how many ways can the racecars finish in first, second,…

A: A automobile race contains 15 racecars.

Q: In how many different ways can the director of a design and structural department choose 2 Civil…

A: Given: Number of applicants to be chosen from 7 applicants are 2. Number of applicants to be chosen…

Q: 2. If you have 7 types of candy, how many pieces of candy would you have to guarantee that you had…

A:

Q: In how many ways can 7 students from a class of 28 be chosen for a field trip?

A:

Q: How many ways can a teacher choose 3 out of 8 students for a field trip?

A: Need to find the number of ways a teacher choose 3 out of 8 students for a field trip.Choosing r…

Q: 4. In how many ways can 5 starting positions on a basketball team be filled with 8 men who can play…

A: The number of men who can play any of the positions is, n = 8 The number of starting positions on a…

Q: 5. How many ways we can choose a heart card out of a regular deck ofa cards

A: In this question, concept of combination is used. Combination A combination may be a mathematical…

Q: In a certain beauty pageant, there are 10 equally beautiful and talented candidates. In how many…

A:

Q: 8. In how many ways can 4 girls and 5 boys sit in a row if the boys and girls must alternate?

A: (8) Number of girls = 4 Number of boys = 5 The arrangement of boys and girls must sit alternate in a…

Q: 6. From a pool of 10 candidates, a company has to choose a president, vice president and a…

A:

Q: How many ways to choose 4 out of the 10 candidates to be sent to a conference?

A: Combination Rule: The arrangement of r objects from n different objects is given by:

Q: 5. A pharmaceutical researcher needs 7 people to test the effectiveness of an experimental drug. If…

A: we have to select people therefore we will use combination nCr=n!/r!(n-r)!

Q: 10. In how many ways can we select a group of 2 men and 3 women out of three men and four women…

A: Determine the number of ways in which 2 men and 3 women out of three men and four women can be…

Q: 4. In how many ways may the judges in a beauty pageant choose a winner and a first runner-up if…

A: The objective is to find the number of ways that the judges can select a winner and a runner-up from…

Q: 10. If there are 15 people and only 2 chairs are available, in how many ways can they be seated?

A: Explanation: Given that,  Number of people=15 Available chairs=2     Formula Used: Crn=n!r!·(n-r)!

Q: In how many different ways can we select a committee of four members from 13 applicants?

A:

Q: How many ways can you choose 5 out of 10 friends to invite to a dinner party?

A: To solve the problem of combinations (selections) in the given scenario.

Q: 7. How many ways are there that in a class of 60 students, 2 students will not have the same birth…

A: Here Given 60 Students  Now Assume that there is 365 Days in one year

Q: In how many ways can a couple invite 3 out of their 15 closest friends to a dinner party?

A:

Q: (3) In how many ways can 5 boys and 2 girls sit in a row if just the girls are to sit together?

A: Permutation is a method in mathematics that is used to find the number of ways in which certain…

Q: 4. Consider a bag containing four red marbles, two green ones, one transparent one, three yellow…

A: Given that there are 4 red marbles, 2 green,1 transparent, 3 yellow, and 2 orange marbles. So there…

Q: 2. In how many ways can five students queue for tickets for a show?

A: The number of ways in which five students queue for tickets for a show is           5!  ways…

Q: How many ways can we award a 1st, 2nd, and 3rd prize among 5 contestants?

A: The total number of contestants is 5. To find the number of ways can we award a 1st, 2nd and 3rd.…

Q: n how many ways could a club of 19 members choose a president, vice president, and treasurer?

A: The club has 19 members. To find the number of ways to choose a president, vice president, and…

Q: In how many ways can a student select 7 out of 10 questions to work on an exam?

A: Given that, The total number of question to work on an exam is, n=10 The student select number of…

Q: how many ways can a group of 4 boys be selected from 9 boys?

A: We have to select 4 boys from 9 boys

Q: 2. In how many ways can three singers and four dancers be chosen to make a team if there are seven…

A: We have to find in how many ways three singers and fours dancers be chosen to make a team if there…

Q: 6. If there are 12 teams in a basketball tournament and each team must play every other team in the…

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

Q: In how many ways can first, second, and third prizes be awarded in a contest with 360 contestants?…

A:

Q: 3. A blood bank needs twenty people to help with a blood drive. Twenty-five people have volunteered.…

A: Topic- Permutation and Combination

Q: In how many different ways can a president, vice-president, secretary, and a treasurer be selected…

A:

Q: In how many ways can 3 students be selected from a group of 12 students to represent a university in…

A: Given data: Total students = 12 3 students  selected  randomly To find: In how many ways can 3…

Q: 1. Four cats and five mice enter a race. In how many ways can they finish with a mouse placing…

A: Given that Number of cats=4 Number of mice=5 To find Total number of ways can they finish with a…