1. A restaurant is preparing a large round table with 2 +1 seats (the seats are unla- belled). The waiter has n + 1 red napkins and n blue napkins. How many visually distinct ways are there for the waiter to place the kins around the table? Give a combinatorial proof that your solution is correct. nap-

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: QUESTION 23 There are 150 seats in the auditorium. 40 located on the left; 50 located on the right;…

A: At least 23 means 23 or 24 or 25.There are 60 seats which are located in the center. So (150-60)=90…

Q: 2 le students have appeared in test a in which the top 3 will get a prise. How mony posible ways are…

A: 1.To find: the number of ways such that 3 persons get prize out of 10 persons. Please post the…

Q: A box contains five cards with even numbers and seven cards with odd numbers. If two cards are drawn…

A: Given : n (even) = 5 n (odd ) = 7 n (total) = 5 + 7               = 12 number of cards drawn with…

Q: Suppose 85% of a certain product actually satisfies the requirement, and we have 25 of such…

A: It is given that n = 25 and p = 0.85.

Q: (2) Give a combinatorial proof of the following: G)-00-0000-00' (i) justify your answer with…

A:

Q: Suppose (an ) is Cauchy and that for all m, k ≥ 100, |am − a k | 0. Does it follow that the…

A:

Q: Consider the permutation (1 2 3 4 5 6 \3 4 5 6 1 2 7)* 1. Express as a product of disjoint cycles.…

A: Given Permutation: 12345673456127

Q: Suppose we have a Boolean formula with 4 input variables. When we draw the Karnaugh map, there are 6…

A: In 2×1 or 1×2, only one literal changes is value. Therefore we have one less literal in each terms.

Q: There are n = 50 students registered for the course 08TI2. It is well known that two students are…

A:

Q: A group of n = 2k people enter a 2-on-2 basketball competition. Before the competition starts, the…

A: In this question we have to find a relation to find number of teams.

Q: of divisiblity.  For all integers a, b, and c, if a|b and a|c then a|(sb + tc) for any integers s…

A:

Q: Show that A5 has 24 elements of order 5, 20 elements of order 3, and15 elements of order 2.

A:

Q: There are five distinct computer science books, three distinct mathe- matics books, and two distinct…

A:

Q: Calculate the coefficient of x7y5zx7y5z in (x+y+z)13(x+y+z)13. (b) In her discrete math class,…

A:

Q: 3. Give combinatorial proof of a k (") = n () k-1

A: We know that the combination formula: C(n,r) = n!/(n-r)!r!

Q: 8. How many ways are there to arrange 12 identical apples and five different oranges in a row so…

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

Q: Show that A5 has 24 elements of order 5, 20 elements of order 3, and 15 elements of order 2.

A: We know that A5 has only even order permutation. A5 has 5!2=60 elements. Now write the partition of…

Q: SHOW THE FULL SOLUTION OF THIS PERMUTATION 3!

A: Given3!

Q: A survey revealed that of the 10,000 people surveyed, 3,200 drank coffee every morning, and 160 of…

A: No, They are not independent events They are Mutually dependent events

Q: (13),0 - (159), using excess-3 codes with 9's complement method.

A:

Q: 6. Prove that the product of an even permutation and an odd permutation is odd.

A: Let S be set on which permutations are defined. Let  α=(x1,x2,...,xk) and  σ=(y1,y2,...yn) be two…

Q: jim has precisely 150 followers. and, all 150 people who follow jim have precisely 150 followers. In…

A: Given that Jim has followers 150 in number. Also, each follower of Jim follows Jim and 149 others…

Q: 4. Explain why if p is prime then Z, is the only subdomain of Z,

A: To prove:If p is prime, Zp is an subdomain(internal domain).

Q: 3. Suppose a, nEZ and 0 < a< n. Prove that - u 1 + a a (:) in terms of factorials; and secondly by…

A:

Q: (5) Suppose thath and k are positive integers and that n = hk. Write a combinatorial proof that (h!)…

A: Suppose h and k are positive integers and that n=hk. Claim: n!h!k is an integer. Proof: Consider the…

Q: 2. A group contains k men and k women, where k is a positive integer. How many ways are there to…

A:

Q: 5 (9 9 () 2. Find a reduced residue system modulo 2", where m is a positive integer. in a reduced…

A: To find a reduced residue system modulo 2m, where m is a positive integer.

Q: 2.4 a. Find all the cluster points of the set Q of all rational numbers, and justify your…

A:

Q: Suppose (an) is Cauchy and that for all m, k ≥ 100, |am − ak| 0. Does it follow that the interval…

A:

Q: 3.(d) Let a, be the number of edges of W, and b, be the number of edges of C, Find a recurrence…

A: Solution of part (d): Given that an is the number of edges of Wn and bn is the number of edges of…

Q: п(п + 1) Show that , k 2 k=1

A:

Q: (A) Compute the (infinite) discrete convolution (-2, –5, –3, –1) • (–4, –4, –5, –4).

A: Use the sum by column method to calculate the discrete convolution .                 Disclaimer:…

Q: A person with $2 in her pocket bets $1, even money,on the flip of a coin, and she continues to bet…

A: Given data :person = $2Her pocket bets $1 , Suppose He bets on head .She gets $1 If geads turn up…

Q: Prove that when you select n +1 numbers from {1,2, ... 2n} two of them must be consecutive (that is,…

A: Use inductive argument and Pigeon hole principles

Q: Exercise 2. Use a combinatorial argument to prove É(:)-("*") n+r+ k=0

A: ∑k=0rn+kk=n+r+1r LHS=n0+n+11+n+22+⋯+n+rr       =n0+n+10+n+11+n+22+⋯+n+rr-n+10       =…

Q: 5) Prove by induction on n7 6 that a square Can be decomposel into n subsgueres (of poosibly…

A: For any n≥6, it is possible to divide a square into n squares.

Q: 7. If that second graph represents six games between four teams, and the score dif- ferences are…

A:

Q: [Q1] From the letters {A, B, C, D, E, F, G}, how many: (a) 3-distinct-letters co can be generated?…

A: Given: There are 7 letters A, B, C, D, E, F, G

Q: Hugh was trying to see if he could tile a 2" x 2" board with L-shaped tiles (i.e. a 2 X 2 tile with…

A: Given: We have given a 2n×2n board and we want to fit the board with L-shaped tiles such that ∃ an…

Q: An organization wants to assemble a cluster of n computers using wires and hubs. Each must have…

A: Solution of the problem as follows

Q: Prove that: there exist infinitely many 5-tuples of practical numbers of the form (n-8, n – 4, n,…

A: It is given that 5-tuples of practical number of the form (n-8, n-4, n, n+4, n+8)

Q: ) Solve the problem by combinatorics .How many different strings can be made from the letters in…

A: Since you have asked multiple question, as per company guidelines we will solve the first question…

Q: Suppose that there are n = 2k teams in an eliminationtournament, where there are n∕2 games in the…

A:

Q: 1. A restaurant offers a meal consisting of one of the three entrees and one of four desserts at a…

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

Q: 18. More Hotel C (ExH). Given the scenario in Mindscape 16-that is, the hotel starts full-suppose…

A:

Q: I. Consider the permutation (1 2 3)(4 5)(1 25 4)-2. 1. Express as a product of disjoint cycles. 2.…

A: consider  the permutation (123)(45)(1254)-2

Q: Provide a combinatorial proof that includes quarternary strings {0,1,2,3} to prove that: (:) - () +…

A:

Counting Principles

In statistics, the counting principle can be said to be the concept in which the quantity of an item is determined. There can be a single item, or a group of items, or items that are related to each other. In every possible set of items, the quantity of the possible item groups or their sorting measures can be determined with counting principles.