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    Combinatorics

    20 Combination Problems

    Please show all work. Classify each problem according to whether it involves a permutation or a combination. 23. In how many ways can the letters of the word GLACIER be arranged? 24. A four-member committee is to be formed from a twelve-member board. In how many ways can it be formed? 27. In how many ways can nine differe

    Mathematics - Algebra - Combinatorics

    Suppose B is a proper subset of C. a. If n(C) 5 8, what is the maximum number of elements ... b. What is the least possible number of elements ... Suppose C is a subset of D and D is a ... Suppose you are playing a word game ... Use a Venn diagram to determine ... Case Eastern Junior College awarded 26 varsity

    Counting Letter Combinations

    Please explain thoroughly. Show or draw diagram. 1. How many four-letter words can be formed from the set of letters{m,o,n,e,y} ? Assume that any arrangement of letters is a word.How many four -letter words can be formed if the first letter must be y and the last letter must be m?( Assume no repetition).

    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