Suppose Set B contains 304 elements and the total number elements in either Set A or Set B is 673. If the Sets A and B have 71 elements in common, how many elements are contained in set A?

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

A: From the given data, the digits that are used for the formation of numbers are : 0,1,2,3,4,5 & 6

Q: Suppose Set A contains 77 elements and Set B contains 59 elements. If the total number elements in…

A:

Q: Suppose Set B contains 32 elements and the total number elements in either Set A or Set B is 54. If…

A: Set theory is a sub branch of mathematics which involves the study of sets. Sets are the collection…

Q: From a club of 17 people, in how many ways can a group of six members be selected to attend a…

A:

Q: Suppose Set A contains 22 elements and Set B contains 24 elements. If the total number elements in…

A: The number of elements in the union of set A and B is equal to the sum of cardinal numbers of the…

Q: Suppose Set A contains 19 elements and Set B contains 15 elements. If the total number elements in…

A:

Q: If 5 out of 7 students at a college are full-time students, what is the enrollment at the college if…

A:

Q: Suppose Set A contains 74 elements and the total number elements in either Set A or Set B is 127. If…

A: Given that, nA=74, nA∪B=127 and nA∩B=17. Note that, the formula for nA∪B=nA+nB-nA∩B.

Q: Students at a private liberal arts college are classified as being freshmen, sophomores, juniors, or…

A: Students at a private liberal arts college are classified as being freshmen, sophomores, juniors, or…

Q: In a certain state, each automobile license plate number consists of two letters followed by a…

A: There are 24 choices for each letter. (this explanation was already shown in the image you shared)…

Q: In a friend group of six, how many ways can we arrange them in a line for a photograph?

A: In a friend group of six, we have to arrange them in a line for a photograph.

Q: With 20 people seated around a tabke, how many ways can 3 people be selected without any being…

A: It is given that there are 20 people seated around a table. The total number of ways of selecting 3…

Q: Suppose Set A contains 76 elements and the total number elements in either Set A or Set B is 122. If…

A: Given data, n(A)=76 n(A or B)=122 n(A and B)=18 n(B)=?

Q: Suppose Set A contains 39 elements and the total number elements in either Set A or Set B is 113. 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: In a different plan for area​ codes, the first digit could be any number from 0 through 3​ the…

A: Given Data: The first digit could be any number from 0 through 3 and  the second digit was either 3…

Q: Suppose Set A contains 23 elements and Set B contains 10 elements. If the total number elements in…

A: Given Information: Set A contains 23 elements. Set B contains 10 elements Total number of elements…

Q: How many 4-digit numbers are there?   And if repetition of digits is not allowed?

A: Given that n= number from 1 to 9 = 9 r = 4 ( since we have to take 4 digit number)

Q: The employees of a company are given a 4-digit identification number. How many different numbers are…

A: GivenThe employees of a company are given a 4-digit identification numberNo.of digits from 0-9=10

Q: If 4 out of 6 students at a college are full-time students, what is the enrollment at the college if…

A:

Q: An overnight express company must include five cities on its route. How many dif- ferent routes are…

A: no. of cities = 5

Q: From a club of 16 people, in how many ways can a group of five members be selected to attend a…

A: Given Data: The number of people in the club is: n=16 The number of members required is: x=5 The…

Q: How many 3-digit numbers can be formed that are greater than 5 hundred and whose last digit is…

A: Given conditions: 3-digit number greater than 500 Last digit is a 3 or 9

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: If repetitions are not permitted, how many 3-digit even numbers can be performed from the six digits…

A:

Q: If there are 1022 different classes at a university, how many different rooms are required in order…

A: according to question, 1022 different classes are there at a university and we have to schedule all…

Q: Suppose a designer has a palette of 14 colors to work with, and wants to design a flag with 4…

A:

Q: From 6 English teachers and 5 Mathematics teachers, committee of 5 teachers will be organized. How…

A:

Q: Suppose Set A contains 88 elements and Set B contains 39 elements. If the total number elements in…

A: There are two sets A and B. n(A)=88, n(B)=39 and n(A or B)=125.

Q: How many elements are in the union of four sets if each of the sets has 95 elements, each pair of…

A: Here, there are four sets. This is representing as A, B, C, and D.Each of the sets has 95…

Q: Suppose Set B contains 395 elements and the total number elements in either Set A or Set B is 659.…

A: Given setB=395 Total number of elements=659 Common elements=54 SetA=?

Q: An overnight express company must include thirteen cities on its route. How many different routes…

A:

Q: Suppose Set B contains 76 elements and the total number elements in either Set A or Set B is 104. If…

A: Given that: Number of elements in set B = 76 Number of elements in set A or set B = 104 Number of…

Q: Suppose Set B contains 335 elements and the total number of elements in either Set A or Set B is…

A: Given  Number of elements in B = 335  Number of elements in either set A or set B = 608 number of…

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

A: Given that, Man has 8 shirts and 3 ties How many different combinations can he wear?

Q: Suppose Set B contains 31 elements and the total number elements in either Set A or Set B is 126. If…

A: Given that,  nB=number of elements in set B=31nA∪B=number of elements in set A or set…

Q: How many license plates can be made using either two or three letters followed by either two or…

A:

Q: Suppose a designer has a palette of 15 colors to work with, and wants to design a flag with 5…

A: Given that a designer has a palette of 15 colors and he wants to design a flag with stripes, all of…

Q: Suppose Set B contains 95 elements and the total number elements in either Set A or Set B is 103. If…

A:

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: How many unordered sets are there of four items chosen from eight

A: According to the given information in this question We need to find the value of C(8,4)

Q: Suppose Set A contains 90 elements and Set B contains 88 elements. If Sets A and B have 20 elements…

A: Given that Set A contains 90 elements and Set B contains 88 elements.  Also given that Set A and Set…

Q: Suppose Set B contains 60 elements and the total number elements in either Set A or Set B is 82. If…

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: Suppose Set A contains 477 elements and the total number elements in either Set A or Set B is 881.…

A: Number of elements in set A= 477  Number of elements in either set A or set B=881 Number of elements…

Q: In a certain state, license plates each consist of 3 letters from the English alphabet, followed by…

A: There are 26 letters (A-Z) in the English alphabet and 10 digits (0-9).   Use the fundamental…

Q: Suppose Set A contains 343 elements and Set B contains 312 elements. If Sets A and B have 89…

A: Cardinality of set A is: A=343 Cardinality of set B is: B=312 Cardinality of set A and set B is:…

Q: How many 5 letter "words" can be formed if exactly 2 of the letters are vowels if order is…

A: There are 5 vowels and 21 consonants. Here, the order is important.

Q: 3) Suppose Set A contains 60 elements and Set B contains 59 elements. If the total number elements…

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”.