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Combinatorics

Counting strings

How many bitstrings of length 10 are there that contain 5(or more) consecutive 0's or contain 5(or more) consecutive 1's? Justify your answer.

Standard Combinatorics

Problem 1) We have 20 kinds of presents; and we have a large supply of each kind. We want to give presents to 12 children. It is not required that every child gets something; but no child can get 2 copies of the same present. In how many ways can we give presents? Problem 2) List all subsets of {a,b,c,d,e} containi

Counting and Combinations

Problem 1) How many bits does 10^100 (ten power one hundred) have if written in base 2? problem 2) Find the number of all 20-digit integers in which NO two consecutive digits are the same Please explain to me the steps, don't just give me the answer, thank you very much.

Set Partitions and Bit Strings

Which of these collections of subsets are partitions on the set of bit strings of length 8? a) The set of bit strings that end with 00; the set of bit strings that end with 01; the set of bit strings that end with 10; and the set of bit strings that end with 11. b) The set of bit strings that end with 111; the set of bit

Abstract Algebra : Permutations

A-Prove that if F is a permutation on A, then F^-1 is a permutation on A. B-Prove that if F is a permutation on A, then (F^-1)^-1 = F

Combinations

A representative of the Environmental Protection Agency wants to select samples from 10 landfills. The director has 15 landfills from which she can collect samples. How many different samples are possible?

Set Operations

1. Write the following in roster form: Set N is the set of natural numbers between ten and sixteen 2. Express the following in set builder notation: Z = {2, 3, 4, 5, 6, 7, 8, 9, 10} 3. For sets A and B, determine whether A = B, A is a subset of B, or B is a subset of A

Interval Notation Question

Write the sets attached using interval notation. If the set is empty, write O. a) The intersection of D and C, where D = {x|x <= -3} and C = {x|x >= 2}. b) {x|x < 3 and x >= 4}

Combinations

1. The coefficient of x^7y^2 in the expansion of (2x-y)^9 2. How many subsets of {2,3,5,7,11, 13, 17,19,23) contain four numbers? 3. If a committee varies its meeting days, how many meetings must it schedule before we can guarantee that at least two meetings will be held on the same day of the week?? 4. How many differe

Show that a set of real rational functions is a field.

NOTE: In this description, R represents the symbol for the set of real numbers. I couldn't find a way to type or copy the correct R symbol for the set of real numbers. Also, the parentheses in R(x) is used to distinguish the ring R(x) of rational functions from the ring R[x] of polynomials. Show that the set R(x) of rational

Graphs, Digraphs, Trees and Forests

I am posting one problem from Exercise 2.2, I need answer for 2.9. I am posting another question from Exercise 3.1: Problem 3.2.) Prove that a graph G is a forest if and only if every induced subgraphs of G contains a vertex of degree at most 1. Problem 3.1) Draw all forests of order 6. See attached file for full pr

Combinations and Permutations

1) Identify each of the following 1) as a permutation or combination and 2) as with or without replacement: a) Social security numbers b) Books in your backpack c) Numbers chosen for the "Big" lotto d) The cards in your hand for a card game e) Lunch chosen by a student from the cafeteria menu 2) A

Statistics Problem Set

See attached file for full problem description. 1. If A &#61645; B and B &#61645; C, what can you conclude? Why? What if A &#61644; B and B &#61644; C? If A &#61645; B and B &#61644; C? 2. Write down all possible subsets of {a, b, c, d} 3. Without writing them down what are the number of subsets of the set A = {a, b,

Permutation or Combination Calculations

For each question determine if the situation is a permutation or combination and if it is with or without replacement, then determine the answer. 1 Identify each of the following 1) as a permutation or combination and 2) as with or without replacement: a) Social security numbers b) Books in your backpack c) Numbers chosen

Combinations

A committee of size seven is to be selected from a group of ten people. In how many ways can this be done?

Discrete Math : Combinations, Permutations and Probability (25 MC Problems)

This test consists of 25 equally weighted questions. 1. Given a two-step procedure where there are n1 ways to do Task 1, and n2 ways to do Task 2 after completing Task 1, then there are _________ ways to do the procedure. a. n1 + n2 b. n1 log n2 c. n1 * n2 d. n12 2. How many bit strings of length 10 begin with 1101? a.

Combinations, Permutations and Cycles

How many elements of order 5 are there in S_8? - I think there are 8! / 3!5! = 56 ways to order the elements in the cycle but how many of order 5 are there? keywords: S8

Permutations and Disjoint Cycles

Let b be the permutation (1 2 3)(4 5 6 7)(8 9 10 11 12 13) what is b^99 as a product of disjoint cycles. -I know b^99=b^3 but I'm a little confused on the disjoint cycles part.

Combinations

A license plate in a certain state consists of a number followed by three letters followed by two additional numbers in the pattern #LL L##. How many possible license plates are there in this system?

Combinations

Suppose you have 10 pairs of slacks from which to choose. How many different ways of selecting a pair of slacks do you have during a period of seven days?

Combinations

2. A seven-person committee composed of Adam, Betty, Cameron, David, Edward, Fritz, and Grace is to select a chairperson, secretary, and treasurer. How many selections are there where Betty is the chairperson, and Adam and Edward are not officers? 12 20 24 210 None of the above

Isomorphisms, Cyclic Groups and Groups of Permutations

Consider the group Z[4] × Z[6] under * such that (a, b) * (c, d) = (a +[4] c, b +[6] d). (here +[4] means + is in Z[4] and +[6] is in Z[6]) We would like to find a group of permutations that is isomorphic to Z[4]Z[6]. Is this group cyclic? If so, prove it. If not, explain why. Do I need to list all the members and ch

Combinations Word Problems

A young boy sends his brother to pick 5 game-boy cartridges from his collection of 10 arcade and 5 sports games. How many ways are there that his brother will select 2 sports and 3 arcade games respectively?