17) How many elements are in the union of four sets if the sets have 100, 150, 250, and 400 elements, respectively, each pair of the sets has 15 elements in common, each triple of the sets has 5 elements in common, and 2 elements are in all four sets?

Q: How many strings of length 5 can be formed if the alphabet (set of available characters)is {a,b,c}…

A: When there are nth places and m elements. With repetition, the choice of 1st place will be m, the…

Q: If a given set has 15 elements how many of its subset have at most two elements

A: Given, No of elements=15  how many of its subset have at most two elements

Q: 9. Consider the 8-elements set A = {a, b, c, d, e, ƒ, g, h} . How many subsets of set A have 4…

A: Solution

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

A:

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

A: Total number of marbles = 4+2+1+3+3 = 13

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

A:

Q: There are 20 seniors serving the student council of a certain school. Of the 20, 3 have not served…

A:

Q: How many subsets with an odd number of elements does a set with 12 elements have?

A: Given that a set contains 12 elements. We need to calculate the total number of subset with an odd…

Q: How many strings of four decimal digits a) do not contain the same digit twice? b) end with an even…

A:

Q: If three alphabets are to be chosen from A, B, C, D and E such that repetition is not allowed then…

A: In question, Given that A, B, C, D and E are 5 alphabets then three alphabet are chosen from them…

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

A: Given, four red marbles,three green ones, one transparent one, three yellow ones, and three orange…

Q: How many four​-digit numbers may be formed using elements from the set​{1, 2, 3, 4, 5, 6, 7, 8​} if…

A:

Q: Consider an alphabet that has 21 consonants and 5 vowels.  In how many ways can you make any…

A: This is from combinatorial.

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: Suppose A₁, A2, ..., A30 are thirty sets each having 5 elements and B₁, B₂, ..., B₁ are n sets each…

A: Given that A1, A2, . . ., A30 are thirty sets each having 5 elements and B1, B2, . . ., Bn  are 'n'…

Q: How many ways are there to select three unordered elements from a set with five elements when…

A: Given: Number of elements = 5 Number of unordered elements = 3 If repetition is allowed,…

Q: A club has seven members. Three are to be chosen as a group to a national meeting. A) If the club…

A: Given Information:  Number of members in a group = 7  Number of men = 4  Number of women = 3

Q: In how many ways can they line up so that no two geese are standing next to one another? (There is…

A: There are 10 ducks and 6 geese.

Q: How many unordered sets are there of two items chosen from four? sets

A: To Find: How many unordered sets are there of two items chosen from four? Concept: Crn=n!r!n-r!

Q: How many four​-digit numbers may be formed using elements from the set ​{1, 2, 3, 4, 5, 6, 7​} if…

A:

Q: How many subsets are there of the set N = {5, 42}?

A: We ahave to find no. Of subsets.

Q: a committe of 4 is to be selected from 6 men and 5 women. 1 particular man and 1 particular woman…

A: From the given information, there are 6 men and 5 women. That is, the total number of persons is…

Q: How many subsets with an odd number of elements does a set with 10 elements have?

A: To find the total number of subsets with an odd number of elements of a set with 10 elements, first…

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…

A:

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

A:

Q: A. How many 3-digit numbers can be formed from the set of decimal digits if the numbers formed are…

A: Answer is given below:

Q: How many subsets of set S = {1, 2, 3, 4, 6} do not contain odd numbers? Use bijection to solve this…

A: Solution S={1,2,3,4,6}

Q: An order for an iPad Pro can specify any one of two sizes (iPad Pro 11‑inch, iPad Pro 12.9‑inch),…

A: Given data: An order for an iPad Pro can specify any one of two sizes (iPad Pro 11‑inch, iPad Pro…

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: How many strings of three decimal digits

A: Strings of three decimal digits:

Q: In a set of eleven elements, two subsets A and B shall be determined, such that A contains 6…

A: Let U denote the set of eleven elements,  A is subset of U containing 6 elements and B is the set…

Q: How many three​-digit numbers may be formed using elements from the set​{1, 2, 3, 4, 5, 6, 7, 8, 9​}…

A: given:  set ​{1, 2, 3, 4, 5, 6, 7, 8, 9​}   if no element may be used more than once in a number and…

Q: A product code consists of a string of 4 different letters selected from the set {S,T,U,V,W,X}. How…

A: The number of ways to arrange r objects selected from n distinct objects is given by the permutation…

Q: How many numbers must be selected from the set {1, 2, 3, 4, 5, 6, 7, 8} to guarantee that at least…

A:

Q: How many three​-digit numbers may be formed using elements from the set​{1, 2, 3, 4, 5, 6​} if…

A: Given data: Set{1,2,3,4,5,6} To find: Three​-digit numbers  formed using elements from the set​.

Q: For some particular website, the password must start with one of the letters W, X, Y, or Z. Then…

A: As the English alphabet has 26 letters from A to Z, and there are 10 digits from 0 through 9, total…

Q: How many subsets is obtained from a set with 5 elements?

A: Given n=5

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: Set A contains 6 elements, set B contains 12 elements, and 4 elements are common to sets A and B.…

A: Set A contains 6 elements, set B contains 12 elements, and 4 elements are common to sets A and B.…

Q: 8. There are three places P, Q and R such that 3 roads connects P and Q and 4 roads connects Q and…

A:

Q: Assume that X={A,F,H,D,C} and Y={5,9,4,2,3}. A code consists of 4 different symbols selected from X…

A:

Q: 2) How many elements are in the union of 5 sets if the sets contain 10,000 elements, each pair of…

A: Given that there are 5 sets and sets contains 10,000 elements, each pair of sets has 1000 elements,…

Q: Suppose we have four sets with sizes 50, 60, 70 and 80. Each pair of sets has five common elements…

A:

Q: How many three-digit numbers can be constructed from the digits 0, 1,2,3,4,5,6,8,9 if the number…

A: Given digits is0, 1, 2, 3, 4, 5, 6, 7, 8, 9Total no.of digits=10

Q: How many six-number combinations can be generated from the numbers from 1 to 42 inclusive, without…

A: Given information: A 6 number combination is to be generated. The possible numbers are selected…

Q: Consider a bag containing seven red marbles, two green ones, one transparent one, seven yellow ones,…

A: Determine the number of sets of five marbles include at most one of the red ones but no yellow ones.…

Q: (1point) How many elements are in the union of four sets if each of the sets has 99 elements, each…

A: To find: The number of elements are in the union of four sets if each of the sets has 99 elements,…

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”.