Suppose that every student in a discrete mathematics class of 31 students is a freshman, a sophomore, or a junior. Prove that there could be at least 12 freshmen, at least 12 sophomores, or at least 13 juniors.

Q: Suppose that there are nine students in a discrete mathematics class at a small college a) show that…

A: Given: 9 students in a discrete mathematics

Q: Suppose that there are 6 people in a room. Show that one can always find a group of 3 people such…

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Q: 2. Let S be the set [9] = {1.2..9}. 1 (D) How many derangements of S have 9 in the 2nd position and…

A: We have the set 9=1,2,...,9 We need to find the number of derangements. There are 9 places to fill…

Q: How many people would you have to have in a group so that there is a probablity of at least 0.5 that…

A: The probability should be at least 0.50.5. Consider total n people are selected at random. The…

Q: 2. Finite subsets of Rd are closed.

A: Here we have to prove that any finite subset of ℝd is closed. Here we can use that union of close…

Q: Suppose that four microchips in a production run of fifty are defective. A sample of six is to be…

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Q: 1. Suppose a team X plays 19 games im a two-week period of 14 days, and plays at least one game per…

A: Solution: Given: X plays 19 games in a two-week period of 14 days, and plays at least one game per…

Q: Determine the number of permutations of the set {1 ,2 ,..., 14} in which exactly 7 integers are in…

A: Solution-:

Q: The five most common words appearing in spam emails are shipping!, today!, here!,available, and…

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Q: 1. Will there be at least two people who celebrate their birthday on the same day Yes, definitely O…

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

Q: Suppose that 100 lottery tickets are given out in sequence to the first 100 guests to arrive at a…

A: given  number of lottery tickets = 100 according to question, number of winning tickets = 12 the…

Q: Show that the set {2/3,1/3,2/9,1/6...} is countable

A: Given set of numbers{2/3, 1/3, 2/9, 1/6...}. Here, this set of rational numbers will be proved as…

Q: 1. Suppose three cards are selected from a standard deck of 52 cards and laid out in a row on a…

A: A combination is a selection of items from a group of items, where the order of selection is not…

Q: 4. Find the minimum number of students in a class to be sure that three of them are born in the same…

A: We have to apply the pigeon hole principle to solve this problem.

Q: Suppose that in a particular Finite course, 5/14 of students plan on majoring in math, 11/42 plan on…

A: Given information- We have given the proportion of particular Finite course. P (Major in math) =…

Q: Show that the subugroup generated by any two distinct elements of order 2 in S3 is all of S3.

A: We have to show that the subgroup generated by any two distinct elements of order 2 in S3 is all of…

Q: Show that gcd (f1,..., fa) = gcd ( f1, gcd (f2, ... , f,)) for any s > 3.

A: The greatest common divisor of two numbers a and b is the number that divides both a and b. It is…

Q: The five most common words appearing in spam emails are shipping!, today!, here!,available, and…

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Q: If any subset of size five is chosen from {1, -1, 2, -2, 4, -4, 8, -8), then prove that each of the…

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Q: Show that for all n:  ceil(n) = -floor(-n)

A: In the given question we have to prove that ceil(n)=-floor(-n) That is…

Q: A sonnet is a 14-line poem in which certain rhymingpatterns are followed. The writer Raymond…

A: a). How many sonnets can be created from the 10 in the book? There are 10 possibilities for each 14…

Q: If you have n random real number in a ordered list {a_1,a_2,…,a_n} , what is the probability of…

A: Given n random real number in a ordered list {a_1,a_2....a_n} {a_1,...a_i} is a monotonically…

Q: What is the minimal number of people needed in a class to ensure that there are two students with…

A: Given information: To ensure that there are two students with the same birthday (the same month and…

Q: Suppose that there exists a neighborhood of k > 5 houses, arranged in a circle. The landlords want…

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Q: Show that if there are 8 people in a room, then at least two of them must have been born on the same…

A: There are 7 days in a week.  So we can have 7 people who can have different birthdays from Sunday to…

Q: Let (2,+) be agroup of integers and cn) be acyclic Subgraup of C(2,+), Then one of the following is…

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Q: Let (P, C, K, E, D) be a cryptosystem such that #K = #P = #C. Show that if this cryptosystem has…

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Q: Consider lists made from L, a, T, e, X, with repetitions allowed. How many 4-lists are there in…

A: Please refer to the image below.

Q: Show that among any 4 n−1 people, there are either some n of them who mutually know each other, or…

A: Pigeonhole Principle  :  Simple form Theorem 1  :  If n + 1 objects are put into n boxes, then at…

Q: Show that the weighted arithmetic mean of first 'n' natural numbers whose weight are equal to the…

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Q: For all s, Isin s≤ 1

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Q: From

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Q: 8. Show that, at the n stage of the construction of the Cantor Middle- Thirds set, the sum of the…

A: Cantor Middle-thirds set: It is created by repeatedly deleting the open middle thirds of a set of a…

Q: Construct a Venn Diagram for the scenario. Suppose that a total of 208 students are enrolled in a…

A: Topic:- Sets theory

Q: The five most common words appearing in spam emails are shipping!, today!, here!,available, and…

A: It is mentioned that 1 in every 10 messages is spam. Hence, the probability that the message is spam…

Q: How many ways are there to form a subset of (n| of size k with the property that each selected…

A: Let us define some events   A:- box 1 is selected B:- box 2 is selected E:- Yellow ball is selected

Q: estion 24 According to the Pigeonhole Principle, among any group of 8 people, there must be at least…

A: according to pigeonhole principle

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: Suppose that in a particular Finite course, 4/7 of students plan on majoring in math, 25/42 plan on…

A: Given that, in a particular finite course, 47 of students plans majoring in math, 2542 plans…

Q: Suppose that in a particular Finite course, 4/7 of student plan on majoring in math, 25/42 plan on…

A: Given Information- 4/7 of student plan on majoring in Math, 25/42 plan on majoring in…

Q: Prove that among any group of people, there are always two people with the same number of friends…

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Q: Suppose that every student in a discrete mathematics class of 25 students is a freshman, a…

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Q: Suppose that 150 people celebrated their birthday in three months, where 65 people celebrated their…

A: Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts.  In case…

Q: Suppose that for each prime p, Zp is the homomorphic image of agroup G. What can we say about |G|?…

A: Concept: A branch of mathematics which deals with symbols and the rules for manipulating those…

Q: O does NOT have a multiplicative ìnverse

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Q: a. Show that in any group of 50 or more people there are at least 5 of them with the same birth…

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