A family with three children are to pose for a family picture in a row. la) In how ways can they be arranged if they can take any position in the picture to be taken? (b) In how many ways can they be arranged in a row if the mother and father will stay at both ends? (C) In how many wavs can they be arranged if they take two rows where the parents will stay at the front row?

Q: Both of my friends Abu and Deps will be part of the group? Only one of them will be part of the…

A: Here use combination for given problems

Q: A committee of 4 students is to be made. There are 5 boys and 5 girls available for selection. In…

A:

Q: a. A coin is tossed 3 times. Find out the number of outcomes. b. In how many ways can the letters of…

A: a) When tossed a coin 3 times then  then we have possible combinations of outcomes  are - { HHH,…

Q: If there is 1 person in a room and no one shakes his or her hand, and then someone else enters the…

A: Let n be the number of persons in the room.

Q: A family with three children are to pose for a family picture in a row. A.in how many ways can they…

A:

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

A:

Q: In how many ways can a chairperson and a treasurer be chosen from a club with 18 members, all of…

A: Total number of members is =18

Q: A troupe of  12  dancers is going to line up on stage. Of these dancers,  6  are wearing black and…

A: By using the knowledge of permutations we can solve the problem.

Q: 3. In how many ways can a committee of committee must have 3 seniors? formed from 4. A box contains…

A: Given,no.of juniors=5no.of seniors=7Total no.of peoples =12

Q: A group of 10 friends go out for dinner at a fancy dining room and they each leave their hat with an…

A: To find In how many ways can the coat room clerk return the hats so that everyone receives the wrong…

Q: Four married couples have bought 8 seats in the same row for a concert. In how many diff ways can…

A: Given: Four married couples have bought 8 seats in the same row for a concert.

Q: A woman has 11 close friends. In how many ways can she invite 5 of them to dinner if two of them are…

A:

Q: In how many ways can 3 Americans, 4 Frenchmen, 4 Danes, and 2 Italians be seated in a row so that…

A: We have given that  Americans = 3 Frenchmen = 4 Danes = 4 Italians = 2

Q: A sales assistant is hanging  11  sweaters on a rack. He has  5  green sweaters,  3  pink sweaters,…

A: In how many distinct orders can the sweaters be arranged if two sweaters of the same color are…

Q: how many ways can 5 textbooks, 3 coffee table books and 2 novels be arranged if the textbooks must…

A: This question is from permutation We have to calculate, in how many ways 5 textbooks, 3 coffee table…

Q: Suppose 7 of the 15 players are left-handed. How many ways are there to select 3 left-handed…

A:

Q: you had a box of five different kinds of fruit and you could choose 2, you might get an apple and an…

A: Given that  Number of types of fruits (n) = 5 Number of fruits we could choose = 2   We know that…

Q: a contractor builds homes of 9 different models and presently has 3 lots to build on. In how many…

A: Given: A contractor builds homes of 9 different models and presently has 3 lots to build on.

Q: In how many ways can 7 children and 6 mother be arranged in a row so that:  No two children are sit…

A:

Q: In how many ways can 8 people be seated in a row if there are two women and these women should sit…

A: Total number of people = 8 Two women are seated in first and sixth place. Now, there are only 6…

Q: 2. How many different arrangements can be made by using all the letters of the word MATHEMATICS ? 3.…

A: Here use combination

Q: In how many ways can you seat two children and three adults in a row of five seats if the children…

A: Number of ways of arranging two children       =2! Number of ways of arranging three adults…

Q: an insurance agent has a list of 7 prospects and decides to telephone 5 of the prospects today and…

A: Firstly, find the number of different ways in which the agent can telephone the 5 prospects today.…

Q: Suppose we want to choose 5 objects, without replacement, from 15 distinct objects. 1) How many…

A: Provided information is ; number of objects(n) =15 For Case 1] : if the order of the choices is…

Q: 4 students go to a theatre and they buy tickets from a row with seats numbered from 1 to 16 but no…

A: To find number of ways were seated numbered from 1 to 16 but no two of them will have adjacent seat.

Q: Assume that the student has a cup with 6 writing implements: 3 pencils, 2 ball point pens, and 1…

A: 1) According to the combination rule, if r distinct items are to be chosen from n items without…

Q: As a vacation souvenir, a family of 4 members wanted to be photographed together with their 2 pets…

A: A family of 4 members wanted to be photographed together with their 2 pets (a cat and a dog). Given,…

Q: .There are four couples want to have their dinner in a round table . In how many ways can they…

A: From the given information, there are four couples want to have their dinner in a round table. Note:…

Q: A woman wants to select 5 pair of shoes from six pairs of red shoes, 4 pairs of white shoes and 3…

A: Pair of shoes women want is 5. Pair of red shoes is 6. Pair of white shoes is 4. Pair of black shoes…

Q: 8. In a fruit feast among 200 students, 88 chose to eat durians, 73 ate mangoes, and 46 ate litchis.…

A:

Q: Each student at State College has a student I.D. number consisting of five digits (the first digit…

A: There are totally 10 digits, the first digit has 9(Because first digit is nonzero) choices. Since…

Q: a. Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed? b.…

A:

Q: A woman has 11 close friends. In how many ways can she invite 5 of them to dinner if two of them are…

A:

Q: 1. A baseball team that has 15 players on its roster. Nine players will be selected for their…

A: Given that  Number of people on its roster (n) =  15 Number of left handers = 5 Number of right…

Q: In a conference, 3 Thai, 4 Japanese, and 2 Filipinos found themselves grouped together in a…

A:

Q: Your friend wants you to be the photographer at his wedding ceremony. During the photoshoot session,…

A:

Q: License plates in a particular state are to consist of 3 digits followed by 2 uppercase letters. How…

A: no.of digits=10  (0 to 10)no.of uppercase letters=26   (A to Z) 9 ways fill it (0 , 2, 3...10) 9…

Q: The principal wants to have a teacher committee on non-semestering. There are 11 secondary teacher…

A: Determine the number of ways that the principal can form a committee of 5 if there must be at least…

Q: Suppose we want to choose 6 objects, without replacement, from 9 distinct objects. (a) If the order…

A: Solve

Q: 4. Six people attend the theater together and sit in a row with exactly six seats. a. How many ways…

A:

Q: In how many ways can 7 male students be arranged in a row if Hanz and Fitch insist next to each…

A:

Q: A committe of 5 members is to be formed out of 6 gents and 4 ladies. In how many ways this can be…

A: Given: Total Gents = 6 Total Ladies = 4 Required 5 members committee for the at least two ladies

Q: Four married couples have bought 8 seats in the same row for a concert. In how many ways can they be…

A: Given: Number of seats = 8

Q: In how many ways can 3 blue books and 4 red books be arranged on a shelf if a red book must be on…

A: The number of ways in which n different objects can be arranged, is given by n!, where,…

Q: How many possible ways can a housewife take to buy a book from a bookstore, then buy groceries from…

A:

Q: 1. A group of 9 people consisting of 4 mothers and 5 children bought tickets for the cinema in the…

A: Given, 4 Mothers and 5 Children

Q: In how many ways can a committee of 9 students be chosen from 8 juniors and 10 seniors if there must…

A: NOTE*** As per bartleby guidelines for more than one question asked only first to be answered, send…

Q: company’s CEO has 8 people reporting directly to her, and she wants to select 2 to attend the grand…

A:

Q: There are 10 men and 8 women in a department (a) In how many ways can the 10 men and 8 women be…

A: (a) Consider the 3 men separately. And 7 men and 8 women are remaining. They cannot re-arrange since…

Q: An algebra class has 12 students and 12 desks. For the sake of variety, students chang thhe seating…

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.