2. Consider the collections C = {penny, nickel, dime, quarter} D = {penny, nickel, nickel, dime, quarter, quarter, quarter} (a) Are the collections C and D equal? Why/why not? (b) If D is a set, explain why we must conclude C and D are equal. (c) What does this say about collections where elements are repeated?

Q: 3. There are 350 farmers in a large region. 260 farm beetroot, 100 farm yams, 70 farm radish, 40…

A:

Q: 2. What is the number of k-digit strings one can form over an n-element alphabet if (a) there are no…

A:

Q: 1. In how many ways can ten items be selected from among fifteen items (a) if order is important?…

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

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

A:

Q: How many ways are there to choose two subsets A and B of [n] so that A ⊆ B, and |B| is even

A: Using logic of sets and subsets we will solve the problem. Using facts we will find a solution to…

Q: In how many ways can we select a committee of five persons from a group of five women and six men…

A:

Q: a. How many students prefer Canvas only? b. How many students prefer at most one platform?

A: We shall find out the answer of the given questions From the table provided.

Q: 10. In how many ways can 3 men and 3 women be seated at a round table if (a) no restriction is…

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

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

A:

Q: What are the number of distinct subsets and number of distinct proper subsets for {a,b,c,d,e,f}?

A: The set contains 6 elements . We know that number of subsets of set of n elements is 2^n. So given…

Q: (b) Every student in a discrete math class is either a computer science or a mathematics major or is…

A: The union of events A and B is defined as n(A ∪ B) = n(A)  + n(B) – n(A ∩ B).

Q: (a) How many ways are there to distribute seven identical apples and six identical pears to three…

A: Given: To distribute seven distinct apples and six distinct pears.

Q: How many proper subsets does S = {A, B, C, D} have?

A: We can find the number of proper subsets as below using the required formula.

Q: 3. Seven numbered red balls and three indistinguishable blue balls are to be placed in five labelled…

A: Given that: Seven numbered red balls and three indistinguishable blue balls are to be placedin five…

Q: A committee of four is to be selected from a group of fourteen people. How many different committees…

A: Out of 16 members, a committee of 4 members can be selected as follows: Thus, 1820 different…

Q: exactly how many subsets does set B={1,2,3,4} have

A: The given set is

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

A:

Q: b . What is the minimum number of cards that must be drawn from an ordinary deck of cards to…

A: b)i) There are 13 ranks. [J,K,Q,A,2,3,4,5,6,7,8,9,10] If we have 2 cards from each rank , then we…

Q: Consider the set X = {A,B, C, D,E, F, G} case 1 How many 4-letter lists from X (with repetition…

A: A set X is given. We have to find the number of 4 - letter lists possible from X if certain…

Q: 2. How many 3 element subsets of the set {a, b, c, d, e, f, g, h, i} contain no vowels?

A:

Q: How many unordered sets are possible that contain three objects chosen from seven?

A: Number of unordered sets that contain three objects chosen from seven = 7C3

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: (a) In how many different ways can the letters of the word combine be arranged? (b) In how many…

A:

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: List all the subsets of (bear, dog, sheep}. O A. (bear, dog, sheep}, {bear, dog), {bear, sheep},…

A: Given set is {bear,dog,sheep} Now, we need to find all the subsets of given set (i.e) the power set…

Q: (8) A certain student organization has 14 members - 4 graduate students and 10 un- dergraduates. A…

A:

Q: 2.24 Students at a private liberal arts college are clas- sified as being freshmen, sophomores,…

A: Given: Students are classified as freshmen, sophomores, juniors and seniors. Hence, number of…

Q: 2. Nine runners are entered in a 100-meter dash for which a gold, silver, and bronze meda will be…

A: Solution: Total number of runners = n= 9  Number of medals = Gold, Silver and Bronge= r= 3

Q: 2. A club has seven members. Three are to be chosen as a group to a national meeting. A) How many…

A:

Q: 22 The parent-teacher's association committee of a school consisting of 6 members is to be formed…

A: We have to apply the concept of combinations to find the number ways in each cases.

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 are there of the set A = {Lilliana, Alyvia, Leanne, Imani, Kaleigh}?

A: Given set A = {Lilliana, Alyvia, Leanne, Imani, Kaleigh}

Q: Explain why in a drawer containing only two different colors of socks one must draw only three socks…

A:

Q: How many distinct proper subsets are there of the set N = {9, 41, 68, 17, 33, 54}?

A: Number of the proper set = 2n -1

Q: 17) How many elements are in the union of four sets if the sets have 100, 150, 250, and 400…

A: Here, n(A)= 100, n(B), 150, n(C)=250, n(D)=400 n(A∩B)=15, n(A∩C)=15, n(A∩D)=15, n(B∩C)=15,…

Q: Suppose that there are 27 students in discrete mathematics class. Show that the class must have at…

A: Here we solve this question by contradiction.

Q: 1. How many ways can you choose 4 numbers from the set p = {4, 6, 8, 10, 12} or 3 numbers from the…

A:

Q: 4. A car dealership has 5 minis (M), 8 convertibles (C) and 14 sedans (S) in its inventory.…

A: Given information: Number of minis(M) = 5 Number of convertibles(C) = 8 Number of sedans(S) = 5…

Q: The vast majority of Visa and Discover Card credit cards have 16-digit card numbers. The first digit…

A: According to the given information The first digit of the card has two choices (4 or 6) Digits 2…

Q: What is the minimum number of students required in a discrete structures class to be sure that at…

A: As we have five grades: k=5 And the number of students: r=9 And we have to calculate: Nk=r N5=9

Q: How many subsets are there of the set N = {1, 44, 65, 11, 39, 53, 26}?

A: Given,          The set is N=1, 44, 65, 11, 39, 53, 26We know that,          The number of subsets…

Q: the collection of the five worst U.S Presidents well defined and a set?

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: 1. In how many ways can a a boy and a girl be selected from a group of five boys and six girls? 2.…

A: According to bartleby policy I have solved first question. I hope it will help you...

Q: {r, e, v, o, I, u, t, i, o, n}_ _{t, o, I, o, v, e, r, u, i, n} {r, e, v, o, I, u, t, i, o, n} V {t,…

A: Here use definition of proper subset

Q: 12. Suppose a list A contains the 30 students in a mathematics class, and a list B contains the 35…

A: list A(Mathematics)=30 studentslist B(English)=35 studentslist A∪B(Both)=20…

Q: 2.22 In a medical study, patients are classified in 8 ways according to whether they have blood type…

A: Given: Number of ways according to blood type =8 Number of ways according to blood pressure =3

Q: 10. If a set has 255 proper subsets, how many elements are there? Why?

A:

Q: 12. How many possible sets of four marbles include no more than 1 purple marble?

A: