Suppose we have four sets with sizes 50, 60, 70 and 80. Each pair of sets has five common elements and each triple of sets has one common element and there are no elements common to all four sets how many elements are in the union of these four sets?

Q: Suppose we want to choose 5 objects, without replacement, from 15 distinct objects.   How many ways…

A: topic -  permutation and combination

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: Assume that you have a committee of 12 members, made up of 3 men and 9 women. In how many ways can…

A: We have to find given probability..

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

A:

Q: Assume that there are 9 girls and 8 boys in the neighborhood club, and a team of 5 is to be…

A: As there are 9 girls and 8 boys now if a team of 5 is to be selected.1) Number of different teams…

Q: 5 identical copies of a movie will be stored on 20 computers such that each computer has at most 1…

A: Given: 5 identical copies of a movie will be stored on 20 computers

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

A: Solution As per guidelines we answer the first question only when questions are different.

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: Assume that you have a committee of 15 members, made up of 9 men and 6 women. In how many ways can…

A:

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

A: We have 6 Red marbles2 Green marbles1 transparent marble4 yellow marbles2 orange marblesTotal no of…

Q: Suppose Set B contains 304 elements and the total number elements in either Set A or Set B is 673.…

A:

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: Assume that there are 8 girls and 12 boys in the neighborhood club, and a team of 6 is to be…

A: Given information: Number of girls, g = 8 Number of boys, b = 12 A team of 6 is to be selected. It…

Q: Assume that there are 11 girls and 9 boys in the neighborhood club, and a team of 8 is to be…

A: It is the question of permutation and combination. And the whole solution is shown below.

Q: Suppose that there are 9 female and 12 male students in a classroom. How many different 5-member…

A: Combination:   A combination is a selection of objects where order is not important.   If n is…

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: 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 Find the sets of five marbles containing 2 yellow marbles:…

Q: If the union of two sets is countable, then each set is also countable.

A:

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

A:

Q: Suppose that a department contains 10 men and 15 women. How many ways are there to form a committee…

A:

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: 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 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: 10 identical copies of a movie will be stored on 40 computers such that each computer has at most 1…

A: Given the statement. 10 identical copies of a movie will be stored on 40 computers such that each…

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

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: Suppose that we have 10 numbered blocks, 2 RED, 3 BLUE, 4 GREEN, and one WHITE.  How many ways can…

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: Find the number of different partitions of a set having 5 elements and  find the number of different…

A: We have to use Bell number. Let S(n, k) be total number of partitions of n elements into k sets. The…

Q: Suppose a designer has a palette of 10 colors to work with, and wants to design a flag with 2…

A:

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: 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: Assume that five men and five women are to sit in a row of ten chairs how many ways can these people…

A: Five men and five women are sitting in a row of ten chairs.

Q: bookshelf has space for exactly 12 books. In how many ways can the books be arranged on the…

A:

Q: Suppose Set A contains 31 elements and the total number elements in either Set A or Set B is 113. If…

A: Given, Two sets, Set A and Set B which contains the no. of elements.

Q: if a given set has 24 elements how many of its subsets have at most four elements

A: There are subsets with 0 elements, 1 element, 2 elements, 3 elements, and 4 elements which are…

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

A: Use combination theorem:

Q: There are 9 periods in each working day of a school. In how many ways can one organize 5 subjects…

A:

Q: Assume that the committee consists of 7 Trolls and 7 Ogres. A subcommittee consisting of 7 creatures…

A: Given the committee consists of 7 Trolls and 7 Ogres.To create a subcommittee consisting of 7…

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.…

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”.