At a college library exhibition of faculty publications, three mathematics books, four social science books, and three biology books will be displayed on a shelf. (Assume they are all different) a) in how many ways can the ten books be arranged on the shelf? Answer is 3,628,800 b) in how many ways can the ten books be arranged on the shelf if books on the same subject matter are placed together?

Q: You are tasked to arrange five different Mathematics books, four different Science books, and three…

A: Given,no.of mathematics books=5no.of science books=4no.of English books=3

Q: In how many ways can a 4-member studernt council consisting of a president, a vice president, a…

A: given that there are 9 students out of which we have to make a 4-members committee for students…

Q: In how many ways can the letters in the word "school" be arranged?

A: It is permutations problem

Q: In how many ways the letters in the word "school" be arranged?

A:

Q: In how many ways can you arrange 4 different Mathematics books, 3 of different Science books, and 2…

A: in how many ways can you arrange 4 different mathematics books, 3 of different science book,and 2…

Q: In how many ways can 7 graduate students be assigned to 1 triple and 2 double hotel rooms during a…

A: We can interpret this question as how to split seven students into groups of 3, 2 and 2.

Q: 3. In how many possible ways can you arrange 5 kilos of rambutan, 2 of kilos lanzones, 4 kilos of…

A:

Q: 5. a) How many 10-letter 'words' can be formed from the letters in SUC ESSFUL, if each letter can be…

A: Given word : SUCCESSFUL Number of letters = 10 Number of C = 2 Number of S = 3 Number of U = 2

Q: How many distinct permutations can be formed from the word "WEDNESDAY"? - In how many ways can 8…

A: here use permutation and concept of total arrangement

Q: In how many ways can you seat 12 people at two round tables with 6 places each? Think of possible…

A:

Q: Kelly has different books to arrange on a​ shelf; 4 ​blue, 2 ​green, and 3red. Answer parts a…

A: Consider the given question, Kelly has different books in which 4 blue, 2 green and 3 red. (a) Find…

Q: Khristelle was able to calculate the total number of 3-digit numbers that can be formed from a given…

A:

Q: Consider three balls and three buckets. In how many different ways can the balls be arranged in the…

A: Given :  Number of balls = 3  Number of buckets = 3

Q: 1.) 150 college freshmen were interviewed. 85 were registered for a Math class, 70 were registered…

A: Given,no.of students registered for a math class=85no.of students registered for an english…

Q: In a party, ten chairs are positioned around a circular table. In how many ways can ten people be…

A: Let, There are ten persons 1,2,3,4,5,6,7,8,9,10. So, total possible seating arrangement in the round…

Q: From the digits 1,2,3,4,5,7 and8 a) How many numbers of four different digits each can be formed? b)…

A: Given  The digits 1,2,3,4,5,7and 8  a). How many numbers of four digits each can be formed. b). How…

Q: (A) How many ways can a 3-person subcommittee be selected from a committee of 9 people? (B) How many…

A:

Q: How many ways can the letters of the word BOULEVARD be arranged in       order? b)How many ways can…

A:

Q: 1. In how many ways can eight people be seated at a round table? In how many ways can eight keys be…

A: We will use concepts of combination and permutation  to get the solution

Q: (b) If the order of the choices is not taken into consideration, how many ways can this be done? (a)…

A:

Q: In Connecticut, auto license plates carry 3 digits followed by 3 letters. (Assume the first digit…

A: Since no restrictions are posted it is taken as digits and letters may repeat. Total number of…

Q: A crew of apollo 17 consisted of a pilot, a copilot, and a geologist. Suppose that NASA had actualy…

A: From the provided information, There are 8 trained pilots and 5 geologists as candidates for the…

Q: A theater was designed to have 24 seats in the first row, 30 seats on the second row, 36 seats on…

A:

Q: 41 children need to be assigned to five Tee ball teams. The league wants each team to have 8…

A: Given that, 41 children need to be assigned to five Tee-ball teams. In order to assign all the…

Q: In a class of 50 students, 20 are math majors, 35 are computer science majors, and 12 are majors in…

A:

Q: 7. Given 10 different English books, six different French books, and four different German books,…

A: Given Data: n(English)=10 n(French)=6 n(German)=4 Total=20

Q: In how many ways can the letters of the word be arranged?

A: There is a total of 10 letters in the word. a=4 D=2 B=2 S=1 i= 1 There are 10! possibilities…

Q: How many different arrangements are there for the eight letters {a, c, f, g, i, t, w, x} ? a. How…

A: a.  since we know the 1st letter is t.  The second letter in the permutation can be choosen in 7…

Q: 1. Analyze and solve each problem. a. How many bracelets with no lock can be formed from 7…

A: 7 different coloured beads can be arranged among themselves in a circularorder in (7−1)!=6! ways.In…

Q: (a) How many three-digit numbers can be formed from the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 if…

A: The counting can be done in 2 different ways, i.e. in first case the 1st digit can be 3 and in the…

Q: 4. In a class of 50 students, 20 are math majors, 35 are computer science majors, and 12 are majors…

A:

Q: How many ways can a three-person executive committee (president, vice-president, secretary) be…

A: The number of member on the board of director  =14

Q: How many ways can you arrange OCONTO  if N and T aren't side-by-side?

A: Here given, Word  OCONTO   There are total 6 letters and 3 times O repeated

Q: In how many ways can the letters in the word ARGOS be arranged?

A:

Q: How many 3-digit numbers can be formed fro allowed? O 6 O 12 O 21 O 27 In how many ways can Naomi,…

A:

Q: In how many ways can 5 students line up for a registration?

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

Q: From a group of 10 men and 12 women, a 10-member committee is formed. In how ways can the committee…

A: Note- As per our policy we can answer only the first 3 sub-parts of a question. If you want…

Q: b. In how many different ways can the letters of the word “Karachi" be arranged such that the vowels…

A: From the given information, b) The letter of word =”Karachi” Vowels in the above letter = {a, a, i}…

Q: In how many different ways can seven keys be arranged on a key ring if the keys can slide completely…

A: Here we have to find the number of different ways can seven keys be arranged on a keyring if the…

Q: If 6 horses are racing at a track, how many ways can 3 horses take place in the top 3 places? O 18 O…

A: Given: Number of horses = 6

Q: In how many ways can 3 different novels, 4 different mathematics books, and 1 biology book be…

A: Arrangement of data can be understand using principle counting methods. It arrangement can be done…

Q: In how many different ways can the letters of MISSISSIPPI be arranged?

A: Given :  MISSISSIPPI Number of times I repeated (n1)= 4 . Number of times M repeated (n2)= 1 Number…

Q: In how many different ways can the letters  of the word NOFIBRE  be arranged

A: Given, the word NOFIBRE   There are 7 different letters in the word NOFIBRE

Q: 3. Given that the digit 7,8,9,10, and 11. How many four digits numbers: (a) i. greater than 9000 can…

A:

Q: (a) In how many ways can 13 cards be selected from a deck? (b) In how many ways can 13 cards be…

A: There are 52 cards in a deck we need to select 13 from a deck of 52 cards 13 cards can be selected…

Q: a. How many three-digit numbers can be formed from the digits 0, 1, 2, 3, 4, 5, and 6 if each digit…

A: Part (a) Calculate the number of three digit numbers formed using the letters 0,1,2.3,4,5,6. The…

Q: In how many ways can you arrange books of the on a shelf if there are 4 of the same kind of Math…

A:

Q: In how many ways can the letters in the word TWEEDLEDEE be arranged? O 362,880 O 15,120 O 30,240 O…

A: Word Given : TWEEDLEDEE There are  1 T 1 W 5 E 2 D 1 L

Q: In how many different ways can the letters of the word “Karachi” be arranged such that the vowels…

A: From the given information, The letters of word =” Karachi” Vowels in the above letter = {a, a, i}

Q: In how many ways can ten people be seated around a circular table if three of them insist of NOT…

A: Given problem:- In how many ways can ten people be seated around a circular table if three of them…

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.