How many elements are in the union of four sets if each of the sets has 95 elements, each pair of sets share 45 elements, each triple of sets shares 25 elements and there are 7 elements in all four sets.

Q: A time traveler can take 3 books with him , and he has 68 books to chose from . How many different…

A: Solution

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

A: There are 6 numbers. The required three digit numbers can be formed using the numbers 1, 2, 3, 4, 5,…

Q: A bag contains three red marbles, two green ones, one lavender one, three yellows, and three orange…

A: At most one of the yellow ones means 0 or 1 yellow ones. There are 3 yellow marbles.  And…

Q: How many elements are in the union of four sets if each of the sets has 98 elements, each pair of…

A:

Q: How many different teams of 44 can be chosen from a group of 1818 children and 1515 adults if each…

A: It is given that the number of children is 18 and the number of adults is 15.

Q: If there is a bird in every branch, there will be an excess bird not on the branch but if there will…

A: Here, it is given to us that: There is a bird for every branch, and if each bird sits on one branch…

Q: How many 7-digit numbers can be made from the digits 1, 2, 3, 4, 5, 6, and 7 if each digit can only…

A: Digits: 1, 2, 3, 4, 5, 6, 7.

Q: How many different teams of 4 can be chosen from a group of 15 children and 17 adults if each team…

A: According to provided data, there is total of 15 children (C) and 17 adults (A). Therefore, the…

Q: There are 2 copies each of 4 different books. In how many ways can they be arranged on a shelf?

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

A: From the above data We are given that Total number of cards = n =52 No of selected cards = r =3

Q: How many numbers can be formed from the digits 1, 2, 3, and 4 if repetitions are not allowed?

A: How many numbers can be formed from the digits 1, 2, 3, and 4 if repetitions are not allowed.

Q: In a family of cats, there are 2 un-cool cats for every 3 cool cats. If these cats have 120 paws…

A:

Q: In how many ways can two admirals, three generals, and four lieutenants can be seated in a row of…

A: Given that In how many ways can two admirals, three generals, and four lieutenants can be seated in…

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

A: no.of digits ( 0 to 9)=10no.of letters(A,B,C,D,E)=5

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

A:

Q: A group of 11 people consisting of 1 freshmen, 3 sophomores, 3 juniors, and 4 seniors are selected…

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Q: There are two copies each of 4 different books. In how many ways can they be arranged on a shelf?

A: GivenTwo copies each of 4 different booksTotal no.of books=2×4=8

Q: How many two-digit numbers can be formed from the digits 1, 2, 3, and 4 if a. no digit is repeated…

A: Given that, Digits are given 1, 2, 3 and 4 a) Two-digit numbers with no digit is repeated: Two-digit…

Q: Six math books, four physics books and three chemistry books are arranged on a shelf. How many…

A:

Q: A family has nine children. If this family has exactly five boys​, how many different birth and…

A: Given,A family has 9 childrens

Q: A parent brings 4 children to a movie and the family sits in a row of 5 seats. How many ways can…

A: There are total 5 members to sit. 4 of them are children and one parent. The parent sit on one one.…

Q: How many outfits can be constructed with 1 shirt, 1 pants, and 1 tie from a wardrobe of 2 shirts, 5…

A: The given problem is based on combination {Because order doesn't matter}. The combination of…

Q: Each marble bag sold by Michael's Marble Company contains 3 blue marbles for every 5 orange marbles.…

A:

Q: How many 2 – digit numbers can be formed from the four integers 1, 2, 3, and 4 if repetition is…

A: Given2-digit numbers to be formedNo.of integers =4           (1,2,3,4)

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

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Q: Each marble bag sold by Deshaun's Marble Company contains 5 orange marbles for every 6 green…

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Q: Three members of an organization volunteered to serve as President, Treasurer and Secretary. In how…

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Q: A committee has 10 members and 4 members must be chosen for a subcommittee. Three of the 10 members…

A: Statisticians/mathematicians use different counting techniques while selecting or arranging members…

Q: A bag contains four red marbles, three green ones, one lavender one, three yellows, and three orange…

A: There are number of marbles in bag: Number of red marbles: 4 Number of green marbles: 3  Number of…

Q: A bag contains three red marbles, three green ones, one lavender one, two yellows, and three orange…

A: Solution: Given information: Red marbles = 3 Green marbles = 3  Lavender  marble = 1 Yellow marble =…

Q: If n∈N and n<2000 , how many numbers n have the property that the sum of the digits of n and the sum…

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Q: A bag contains three red marbles, three green ones, one lavender, two yellows, and three orange…

A: Solution: From the given information, a bag contains three red marbles, three green ones, one…

Q: A bag contains four red marbles, three green ones, one lavender one, three yellows, and two orange…

A: A bag contains four red marbles, three green ones, one lavender one, three yellows, and two orange…

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 elements are in the union of four sets if each of the sets has 98 elements, each pair of…

A: Determine the number of elements is in the union of four sets. The number of elements is in the…

Q: A bag contains three red marbles, two green ones, one lavender one, two yellows, and three orange…

A: It is given that there are three red marbles, two green marbles, one lavender marbles, two yellow…

Q: If n EN and n < 2000, how many numbersn have the property that the sum of the digits of n and the…

A:

Q: A man has eight shirts and five ties. Assuming that they all match, how many different shirt-and-tie…

A: Given,            A man has eight shirts and five ties.

Q: A bag contains 5 red marbles, 2 green ones, 1 lavender one, 2 yellows, and 3 orange marbles.  How…

A: Since we will make sets, so order does not matter. So we will use combination.  Atmost one of the…

Q: Three sets have 5, 10, and 15 elements, respectively. How many elements can their union and their…

A:

Q: A group of 11 people consisting of 2 freshmen, 1 sophomores, 4 juniors, and 4 seniors are selected…

A: Given:A group of 11 people consisting of 2 freshmen, 1 sophomores, 4 juniors, and 4 seniors are…

Q: Suppose an outfit consists of a shirt, pants, and shoes. If you have 4 shirts, 7 pairs of pants and…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: For a Halloween party, each guest can choose from the 6 different kinds of candy to have in a prize…

A: Given,no.of different kinds of candy=8

Q: If an Iphone password can have 4 or 6 digit passwords how many combination can there be if there has…

A: Iphone password can have 4 or 6 digit passwords. There are 10 digits in the number system,…

Q: In how many ways can two admirals, three generals, and four lieutenants can be seated in a row of…

A:

Q: How many four-digit numbers can be formed from the numbers 1, 3, 4, 6, 8, and 9 if repetition of…

A:

Q: a committe of 5 people is to be chosen from a group of 6 men and 4 women how many committed are…

A:

Q: Two freshmen and three sophomores from a sorority will attend a conference. If the sorority has 12…

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”.