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Combinatorics

Example of a Permutation or Combination

Program Selection. A meeting is to be addressed by 5 speakers, A, B, C, D, and E. In how many ways can the speakers be ordered if B must come first? Please show which formula is used.

Simple Permutations or Combinations in Excel

Provide a simple Permutation or Combination problem and use Excel's PERMUT or COMBIN statistical commands to solve your problem. You can find PERMUT and COMBIN commands under Excel (Insert ---> Function ---> Statistical). Show the work.

Counting Techniques for a Limited Menu

A restaurant offers the following limited menu. MAIN COURSE: turkey, spaghetti, meatloaf, shrimp. hamburger VEGETABLES: broccoli, carrots, potatoes BEVERAGES : coffee, tea, milk, soda DESSERTS: sundaes, mousse, pie, brownies IF ONE ITEM IS FROM EACH OF THE FOUR GROUPS, IN HOW MANY WAYS CAN A MEAL BE ORDERED?

Sets - List the elements in the set.1

Write the word or phrase that best completes each statement or answers the question. List the elements in the set. 1. Let U = { q,r,s,t,u,v,w,x,y,z} A = { q,s,u,w,y} B = {q,s,y,z,} C = { v,w,x,y,z} a. (A INTERSECT B') U (B INTERSECT A') B. A'-C Use the formula for the number of subsets o

Relations and sets

1) Find a relation R on a set S that is neither Symmetric nor antisymmetric 2) Let S be a set containing exactly n elements. How many antisymmetric relations on S are there. 3) give a recursive definition of X^n for any positive integer n 4) give a recursive definition of the nth odd positive integer 5) Let g: Z -> Z

Mathematics - Problems with Sets

Please show all steps. Thank you. Express the set using set- builder notation. Use inequality notation to express the condition x must meet in order to be a member of the set. 1. A= { 12, 13, 14, 15, 16,...} 2. A= { 600, 601, 602,...,6000} 3. Calculate the number of subsets and the number of proper subsets for

Set Builders

Please explain. Thank you. Are the Sets equivalent? Justify Your answers. 1. A= { 14, 15, 16, 17, 18,} B= {13, 14, 15, 16, 17} 2. A= { 17, 18, 18, 19, 19,19,20, 20, 20, 20} B= { 20, 19, 18, 17} 3. A= { Larry, Moe, Curly, Shemp} B= { Posh, Sporty, Baby, Scary} Are the sets equal? Justify your ans

Counting and subsets

Use the formula for the number of subsets of a set with n elements to solve the problem. 1. Pasta comes with tomato sauce and can be ordered with some , all, or none of these ingredients in the sauce: {onions, garlic, carrots, broccoli,shrimp, mushrooms, zucchini, green pepper}. How many different variations are available for

Set Notation

Let A= {n element of Z : n=4q+1 for q element of Z} B= {m element of Z : m=8r-3 for r element of Z} Prove: a) A is in B b) B is in A C) A=B in set notation.

Permutations and combinations..

In the design of an electrical product, 7 different components are to be stacked in a cylindrical casing that holds 12 components,in a manner that minimizes the impact of shocks. One end of the casing is designated as the top and the other end the bottom. a) how many different designs are possible b) If the seven compon

Proof for Images of Sets

College level proof before Real Analysis. Please kindly explain each step of your solution. 11. Let f: A --> B, and let {D_alpha: alpha is an element of Delta} an {E_Beta: Beta is an element of pi} be families of subsets of A and B, respectively. Prove that (see attached).

Image of Sets

3. Let f(x) = 1 - 2x. Find (a) f(A) where A = {-1, 0, 1, 2, 3} (b) b(N) (c) f^-1(R) (d) f^-1([2, 5]). (e) f((1, 4]) (f) f(f^-1(f[3,4])))

Counting Bitstrings

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

Combinatorics Color Objects

Problem1) What is the number of ways to color n objects with 3 colors if every color must be used at least once? problem2) prove that for any three sets A,B,C ; ((AB) U (BA))^ C = ((A^C) U (B^C)) (A^B^C) ^ means intersection Please explain the steps, help me under

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.

Combinations of Letters and Digits

Could someone show me how to solve the following. 20. How many different license plates can be made if each license plate consists of three letters followed by three digits or four letters followed by two digits?