How many ways can a group of n people be arranged in a circle that contains k equally distributed seats? Write your answer in terms of n, k and „P and prove the result.

Q: How many ways can we arrange eleven bowling balls numbered 1 to 11 in a circle if the even- numbered…

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Q: Suppose we want to choose 5 objects, without replacement, from 16 distinct objects. (a) If the order…

A: In this question, we want to find the number of ways if the order of choice is relevant and not.…

Q: How many groups can be made from the word ''house'' if each group consists of 4 alphabets?

A: Solution

Q: In how many ways can we arrange 3 boys and 3 girls in a circular table if:  All boys and girls are…

A: Given, 3 boys and 3 girls       To find, In how many ways can we arrange them if all boys and girls…

Q: A 6-volume encyclopedia is to be placed on a shelf. How many incorrect arrangements are there?

A: Note- Since you have posted multiple questions, as per our guidelines we are supposed to answer only…

Q: 10) There are 8 members on a board of directors. If they must form a subcommittee of 6 members, how…

A: Given data 8 members available  We have to select 6 from it for committee Here order of selection…

Q: In how many ways can 6 boys and 6 girls be seated around a circular table if all the no girls are…

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Q: ssume that 8 women and 6 men work in a department at a large company. How many ways can a…

A: Combination formula : The number of ways to select r subject from n is determined by using following…

Q: Six people are about to enter a cave in a single row. In how many ways could the arrange themselves…

A: Given: Six people are about to enter a cave in a single row

Q: 3) In how many ways can a group of 5 men and 2 women be made out of a total of 7 men and 3 women?

A: Given,             A group of 5 men and 2 women be made out of a total of 7 men and 3 ways.

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 how many ways can a committee of five men and four women be formed from a group of six men and…

A: The number of ways can a committee of five men is 6C5.The number of ways can a committee of four…

Q: how many ways can Dr. Yes invite 8 of his friends if he has to invite at most 4 at a time?

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Q: (a) How many ways can a store manager arrange a group of 1 team leader and 3 team workers from his…

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: A class consists of 12 students ​(six boys and six ​girls) and one teacher. In how many ways can the…

A: Here there is a class consists of 12 students where there is 6 boys and 6 girls and 1 teacher We…

Q: In a friend group of six, how many ways can we arrange them in a line for a photograph?

A: In a friend group of six, we have to arrange them in a line for a photograph.

Q: A committee of 5 students is to be selected from 16 students in a fraternity. a. In how many ways…

A: Given that a committee of 5 students is to be selected from 16 students in a fraternity. a We have…

Q: In how many ways can 12 different books be distributed among four chi dren so that (a) each child…

A: Given: Number of books = 12 Number of children = 4

Q: i. Find how many arrangements of all letters can be made from the word “COPROCESSORS“. ii. Find how…

A: Permutation: A permutation of a set of items is an arrangement of those items into a sequence or…

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

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Q: In how many ways can a group of 5 men and 2 women be made out of a total of 7 men and 3 women?

A:

Q: From a club of 16 people, in how many ways can a group of five members be selected to attend a…

A: Given Data: The number of people in the club is: n=16 The number of members required is: x=5 The…

Q: A class has 10 students. How many ways can the class be grouped into 2 groups of equal size.

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Q: In how many ways can a committee of three men and two women be formed from a group of six men and…

A: Given, A group of 6 men and 9 women. To find: Number of ways to formed a committee of 3 men and 2…

Q: What is the number of ways to color n objects with 3 colors if every color must be used at least…

A: Given that there are n objects and 3 colors.   The three colors must be used at least once. That is,…

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: Consider a group of N people. If everyone shakes hands with everyone else, how many handshakes take…

A: The number of people in a group is N.

Q: How many ways can a committee of 4 be selected from a club with 22 members?

A: It is an important part of statistics. It is widely used.

Q: In how many ways can 12 people be divided into 3 groups where 4 persons must be there in each group?…

A: Solution: Given information: n= 12 Total number of people.  There are 3 groups each group has 4…

Q: Suppose the group of twelve consists of five men and seven women. a) How many five-person teams can…

A: A group consist of fire men and sexes women. We have to make a fire person team with 3men and 2…

Q: 1) How many ways can 5 kids divide themselves into groups of two? 2) How about groups of three? 3)…

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Q: in how  many  ways can 5 men and 3 girrls  can be seated  in a round table such that  the   girls…

A:

Q: A committee of size 5 is to be chosen from a group of 6 men and 7 women. (a) How many different…

A: Given that 6 men and 7 women. Total people = 6 + 7 = 13

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: In how many ways could 16 people be divided into five groups containing respectively 4,2,3,6 and 1…

A: There are totally 16 people in which divided into five groups containing respectively 4,2,3,6 and 1…

Q: you have 11 tubs of paint how many distinct color groupings can you make with your paint?

A: Total given colors are   11 Total distinct colors grouping   ?   we can solve this question with the…

Q: How many ways can a​ president, ​vice-​president, and secretary be chosen from a club with 11…

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Q: How many ways can captain, co captain and team manager be assigned to a group of 10 runners at a…

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Q: In how many different ways can 8 people be seated in a circle if 3 people insist on sitting next to…

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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: In how many ways can a group of 5 students be picked from a class of 14 students to represent the…

A: There are total 14 students.  We will pick a group of 5 students from them.   Since it is a group,…

Q: In how many ways can a committee of two men and three women be formed from a group of nine men and…

A: In how many ways can a committee of two men and three women be formed from a group of nine men and…

Q: A deli offers 14 different toppings. How many different groups of 3 can be made?

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Q: 2) A class has 25 students. Each day, three students are chosen to present their work at the board.…

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Q: How many ways can a local chapter of the American Chemical Society Schedules 3 speakers for 3…

A: As Dr. S. N. De said "A permutation of a set is defined as an arrangement of its members into a…

Q: In how many ways can a committee of three men and four women be formed from a group of eleven men…

A: Given,no.of mens=11no.of womens=10

Q: How many ways can a committee of 4 be selected from a club with 10 members?

A: No of ways to select a committee of 4 from 10 members is =? We can select in 10C4 ways.   nCr= n! /…

Q: A bag contains 5 black and 4 white balls. In how many ways can we draw from the bag groups of 3…

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Q: In how many ways can a committee of four men and three women be formed from a group of eight men and…

A:

Q: With a group pf five men and five women, how many ways can they be arranged in a row if men and…

A: Given that  Number of women = 5 Number of men = 5