In a set of eleven elements, two subsets A and B shall be determined, such that A contains 6 elements and B contains 5 elements of which two elements are common in A and B. In how many ways can this be done?

Q: A fleet of nine taxis is to be dispatched to three airports in such a way that two go to airport A,…

A: Given, A fleet of 9 taxis is to dispatch to the three airports A, B, and C also, 2 go to A, 6 go to…

Q: a blood​ drive, 6 donors with type O+ ​blood, 5 donors with type A+ ​blood, and 2 donors with type…

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Q: At a computer store, a customer is considering 7 different computers, 8 different monitors, 9…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: A box contains 15 balls in which seven are green and eight are yellow. If five balls must be drawn…

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Q: How many 3-letter codewords can be formed if: At least one of the letters is to be chosen from the…

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Q: Twelve teachers are to be assigned to three schools. In how many ways can this be done if: a…

A: Given Twelve teachers are to be assigned to three schools

Q: If a dealer randomly picks 5 cards from a standard deck that consists of 52 playing cards and then…

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Q: Suppose that in a certain association, there are 12 elected members of the Board of Directors. In…

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Q: There are five distinct computer science books, three distinct mathe- matics books, and two distinct…

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Q: A committee of six is to be formed from nine women and three men. In how many ways can the members…

A: We need to find how many ways 6 members be chosen out of 9 women and 3 men in which at least one is…

Q: There are five distinct computer science books, three distinct mathematics books, and two distinct…

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Q: From a class consisting of 12 CE majors, 10 ECE majors, and 9 ME majors, in how many ways can a…

A: From a class consisting of 12 CE majors, 10 ECE majors, and 9 ME majors. We want to consist group of…

Q: A clothing store has 13 shirts in 4 sizes: small, medium, large, and extra-large for sale. If it has…

A: Number of ways of selling two small shirts is 2! = 2 Number of ways of selling three medium shirts…

Q: Consider a bag containing five red marbles, three green ones, one transparent one, three yellow…

A: The five marbles(none of them are red or green) to be selected from a bag containing 5…

Q: A class is consist of 12 boys and 10 girls. In how many ways can the class elect 4 members of a…

A: We have given that the class consist 12 boys and 10 girls. Total number of members = 22…

Q: A person can order a new car with a choice of 8 possible​ colors, with or without air​…

A: Permutation and combination are used to calculate the number of possible ways to arrange or select a…

Q: how many different ways can a new car be ordered with regard to these​ options?

A: Here use combination for no.of different ways of new car can be ordered

Q: In how many ways can a committee of 5 be formed from 5 juniors, and 7 seniors, if the committee must…

A: GivenNo.of juniors = 5No.of seniors = 7Total no.of seniors and juniors=12

Q: A computer password must be 3 letters followed by 5 digits (0 through 9). How many different…

A: Note: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: Assuming that no one can hold more than one office, how many selections are possible?

A: select a president, vice-president, secretary, and treasurer out of a club with 15 members.  Here…

Q: A committee of 5 delegates is to be chosen from a group of 17 delgates, 10 of whom are women. If at…

A: If an event can be done in n different ways and if another even can be done in m number of ways,…

Q: From a group of 8 men and 6 women, six persons are to be selected to form a committee so that at…

A: Given information 8 men and 6 women Six persons are to be selected to form a committee

Q: A person can order a new car with a choice of 6 possible​ colors, with or without air​ conditioning,…

A: Solution :-

Q: A club with 5 members is to choose 3​ officers: ​ president, vice-president, and​…

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Q: In an examination paper, there are 7 questions in part A out of which any 4 are Example 48. to be…

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Q: Assume that there are 6 types of upholstery, 2 types of wood, and 5 designs to choose from. Of the…

A: Of the 5 designs, 4 designs permit both a choice of wood and a choice of upholstery. We can pick…

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

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

Q: Refer to a set of five distinct history books, three distinct biology books, and two distinct…

A: Factorial Rule: The total number of ways n different objects can be arranged where the order of the…

Q: 1. How many 3-letter words with or without meaning, can be formed out of the letters of the word,…

A: 1. There are a total of 7 letters in the word 'MACHINE' If the repetition of letters is not allowed,…

Q: Refer to a set of five distinct history books, three distinct biology books, and two distinct…

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Q: A committee of 5 is to be made from 3 students and 6 teachers. In how many ways can this be done a.…

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Q: A student committee is to consist of 2 freshmen, 4 sophomores, 3 juniors, and 5 seniors. If 11…

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Q: A panel for a political forum is made up of 14 people from three parties, all seated in a row. The…

A: Given: A panel for a political forum is made up of of 14 people from three parties. The panel…

Q: A committee of 5 consisting of 3 girls and 2 boys is to be chosen from a class with 15 girls and 10…

A: Given: Total Number of Girls=15Total Number of Boys=10Commitee required 5 candidate in whichNumber…

Q: how many ways are there if a teacher has to select 2 students from a group of of four to represent…

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Q: A  commitee of 2 teachers is to be formed in a school such that there is one male and one female…

A: We can pick a female teacher from 12 female teachers in 12 ways.  We can pick a male teacher from 15…

Q: Suppose a library has at least 6 copies of mathematics book, at least 6 copies of a physics book,…

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Q: 9. A committee of senior and junior executives will be formed to decide on recruitment issues. If…

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

Q: A certain committee consists of 7 people. From the committee, a president, a vice president, a…

A: Solution: We need to choose a committe of a president , a vice president, a , a secretary, and a…

Q: In how many ways can three dogs, four cats, four rabbits and two pigs be arranged in a row so that…

A: Given,no.of dogs=3no.of cats=4no.of rabbits=4no.of pigs=2

Q: A particular brand of shirt comes in 12 colors, has a male version and a female version, and comes…

A: Here , particular brand of shirt comes in 12 colors. It has female version and male version. And it…

Q: A certain brand of shoes comes in 4 different styles, with each style available in 4 distinct…

A: A certain brand of shoes comes in 4 different styles.

Q: How many 4-person committiees can be formed from a group of 8 teachers and 5 students if there must…

A: If there is 1 teacher, then there must be (4-1)=3 students.  We can pick 1 teacher from 8 teachers…

Q: A certain committee consists of 20 people. From the committee, a president, a vice-president, a…

A: Given : A certain committee consists of 20 people Now we have to choose a president, a…

Q: Assume that there are 4 types of upholstery, 4 types of wood, and 5 designs to choose from. Of the…

A: Given: There are 4 types of upholstery                            4 types of wood…

Q: If a single card is drawn from a standard​ 52-card deck, in how many ways can a card other than a…

A: Given data: A standard​ 52-card deck

Q: See picture

A: It is given that there are 10 different computers, 9 different monitors,7 different printers are 4…

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

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Q: If there are 10 people and only 6 chairs are available, in how many ways can they be seated?

A:

Set Theory

Every field in the present world involves a set. The theory of sets was developed by German mathematician Georg Cantor while working on the “problems of trigonometric series”.