8. In a beauty contest, there are 12 semi-finalist from which 5 winners will be chosen. How many ways can the winners be

Q: 38. How many different committees can be formed from 5 professors and 15 students if each committee…

A:

Q: 3. In how many different ways can the director of a design and structural department choose 2 Civil…

A: Given: Number of applicants for Civil Engineers is, n(C1)=7. Number of required for Civil Engineers…

Q: 3. In a sportsfest consisting of 40 males and 20 female members, if they were to pick 1 team leader,…

A: The number of ways r items can be selected out of n items is defined using the formula, C(n,r) . The…

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

A:

Q: 3. In how many ways can a team of six be chosen from 20 players so as to (a) include both the…

A:

Q: 3) In how many ways can three bracelets be selected from a box of ten bracelets?

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: 3. Suppose 1500 runners are in a race. How many ways could the runners finish in 1*, 2nd and 3rd…

A:

Q: 10. In how many ways can you line up 5persons to get on a bus?

A: Given problem Given that   10) In how many ways can you line up 5 persons to get on a bus ?

Q: How many different ways can a club of 20 members select a 3-member officer-nominating committee from…

A: Given Information:  Total members = 20  Number of members to be selected = 3

Q: A race has 10 runners. In how many ways can the first three places be decided?

A: Here use combination

Q: 4) A newly formed company of 24 partners wants to select a President, Vice-President and Secretary.…

A: This Problem can be solved by permutation and combination. Permutation is number of possible…

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: 9. In how many ways can a committee of 5 persons be chosen from 7 ladies and 9 men if there is no…

A: As per Bartleby guideline, we have answered only the first question. If you want to get the answer…

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: Out of 9 children, in how many ways can a family have at least 1 girl?

A: We have given that, 9 children i.e. n=9 and family have at least 1 girl i.e. r=1   Combination…

Q: 2. A jury of 12 people is chosen from a pool of 35 potential jurors can be chosen?

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: In how many ways can a committee of not more than 3 representatives be selected from a group of 16…

A:

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: In how many ways a team of 4 representatives can be chosen in a class of 12 students consisting of 5…

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: 9) From a group of 30 people, a jury of 12 people is selected. In how many different ways can a jury…

A: We use combination formula here to find number of ways to select 12 people out of 30 peoples

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 ways can 7 students from a class of 28 be chosen for a field trip?

A:

Q: Suppose that 9 horses run a race. How many first-, second-, and third-place finishes are possible?

A:

Q: In how many ways can a group of 6 students be selected from 7 students?

A:

Q: Suppose a club has 20 members. a. How many ways can they select a chairperson to lead a small…

A: Since you have asked a question with multiple parts in a single request, we would be answering only…

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: 9. In how many ways can three boys can be seated on five chairs?

A: In question, We'll find the ways in which three boys seated on five chairs. The solution is below,

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: (a) How many committees can be formed? (b) How many committees can be formed with at least 2 men?…

A: here total 8 men and 7 women that is 15 employees in office committee of 4 member has to be formed…

Q: In a survey of 105 people, it was found that 40 have lived only in New York, 35 have lived only in…

A: Given, In a survey of 105 people, it was found that 40 have lived only in New York,  35 have lived…

Q: 5. In a group of 15 students, 5 of them are female. If exactly 3 female students are to be selected,…

A: Some of formulas of Permutation and combination n!=1·2·3..... ·n n!=n ·(n-1)! Prn=n!(n-r)! Crn=n!r!…

Q: In how many ways can three committees of 8 persons be formed from 44 persons if the chosen persons…

A: The number of ways to select  r different objects from n different objects, can be given as, Crn…

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: A club has 11 members. Five are to be chosen to go as a group to a national meeting. If the club…

A: The total members in the club is 11. Of them, 7 are men and 4 are women. The main objective is to…

Q: 26. A committee of 6 officials is to be chosen from 8 men and 7 women. If the committee is to…

A:

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: 6. How many ways are there to select 3 candidates from 8 equally qualified recent graduates for…

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

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

A:

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

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

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: 3. A town orchestra is holding auditions for 3 new flute players and 4 new trumpet players. If 8…

A: It is given that a town orchestra is holding auditions for 3 new flute players and 4 new trumpet…

Q: How many ways are there to select 12 countries in the United Nations to serve on a council if 2 are…

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: (c)        A committee of six is to be formed from nine women and three men. In how many ways can…

A:

Q: 1. In how many ways can 8 members of Board of Directors be chosen from 5 juniors and 7 seniors if…

A: Let us suppose there are three marbles viz. a red, a green and a blue. From these, there are three…

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

A: