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# Combinatorics

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### Combinations of Letters and Numbers : Forming License Plate Numbers

How many different license plate numbers can be made using 2 letters followed by 4 digits selected from the digits 0 through 9, if a) Letters and digits may be repeated? b) Letters may be repeated, but digits may not be repeated? c) Neither letters nor digits may be repeated? Show reasoning

### Relations on a Set : Symmetric Difference and Composite

Suppose that R and S are two relations on the set A = {a, b, c, d}, where R = {(a,b),(a,d),(b,c),(c,c),(d,a)}, and S = {(a,c),(b,d),(d,a)}. Find each of the following relations: a) R (+) S (Symmetric Difference) b) R^2 c) S^3 d) S o R (Composite)

### Counting Techniques Arrangements

I am having a hard time trying to understand an example problem in my math book. The problem goes: In how many ways can 3 white tiles, 2 blue tiles, and 2 red tiles be arranged in a single row?( I also need to assume that the tiles are identical except for color.)

### Sets, Counting & Probability : Subsets and Intersection

Consider the following sets: U = {1,2,3,4,5,6,7,8} A = {2,4,6,8} B = {1,2,3,5,7} Which of the following statements is true? a. A intersection of B is the subset of A b. A intersection of B = 0 c. A is the subset of A intersection of B d. A intersection of B = U

### Sets, Counting and Probability: DeMorgan's Law

The result of using De Morgan's Law to Simplify (S' intersection of T") is: ? a. S' union of T b. S union of T' c. S intersection of T' d. S' intersection of T e. None of the above

### Sets, Counting & Probability : Probability Distribution for a Sample Space

Which of the following is a valid probability distribution for a sample space S = {a,b,c,d} a. Pr(a)=-0.2, Pr(b)=0.5, Pr(c)=0.4, Pr(d)=0.3 b. Pr(a)=0.3, PR(b)=0.1, Pr(c)-0.2, Pr(d)=0.5 c. Pr(a)=0.6, Pr(b)=0, Pr(c)=0.3, Pr(d)=0.1 d. Pr(a)=0.5, Pr(b)=0.2, Pr(c)=0.1, Pr(d)=0.3

### Sets, Counting & Probability : Combinations

In a local election, there are eight candidates for five positions as judges on the Supreme Bench. The number of possible outcomes of the election is:

### Sets, Counting & Probability

Eight Horses are entered in a race. In how many ways can they cross the finish line if ties are not allowed?

### Sets, Counting and Grouping

Out of 30 job applicants, 11 are female, 17 are college graduates, 7 are bilingual, 3 are female college graduates, 2 are bilingual woman, 6 are bilingual college graduates, and 2 are bilingual female college graduates. What is the number of women who are not college graduates but nevertheless are bilingual?

### How different statistical devices can be used in business?

How the following statistical devices can be used in business today? Describe their usefulness and how businessman can be benefit, or how to help them in making sound decisions. (Explain individually) --probability --probability distributions --normal distribution --permutation and combinations

### Combinations Proof : The formula

Show that 2(2^n-1 - 1) is the formula used to determine the number of different ways to deal n distinct playing cards to two players where each player gets at least one card. I want to allow the possibility of giving a different number of cards to each player.

### Combinations : Application Word Problems (5 Problems)

2. A group pf 12 students have been hired by the city this summer to work as ground keepers. (a) During their first week of employment, half will be assigned to pick up garbage down town while the other half go on a training course. The second week, they will switch places. In how many distinct ways can 12 students be assigned

### Finding Possible Set Solutions

1. Write out all possible sets {(a/b)*c | a=5, b=10, and c=2 or 3}. See the attached file.

### Review - Weigthed Voting System: Quota; Banzhaf Distribution; Shapley-Schubick Distribution; Dictators, Veto Power Players, Dummies

PLEASE SHOW ALL WORK FOR SPECEFIC QUESTIONS FOR COMPLETE UNDERSTANDING. 1)FIND THE FOLLOWING WEIGHTED VOTING SYSTEM( 8: 6,3,2,1) A) FIND WHAT PRECENT OF TOTAL WEIGHT IS QUOTA? B) FIND BANZHAF DISTRIBUTION IN PERCENTS? C) FIND SHAPLEY- SCHUBICK DISTRIBUTION IN PERCENTS? D) FIND ALL DICTATORS , VETO POWER PLAYERS

### Factorials, Combinations and Permutations

Solve and please show all work: A) 7!-4! B) 20!/18! C)7P3 D) 4P4 E) 8C8 F) 9C5

### Finding Different Combinations

Imagine you've been left in charge of an ice cream stall and you have three flavours of ice cream to sell - vanilla, strawberry and chocolate. If you're selling triples (a cone with three scoops) how many different combinations can you sell?

### Well Ordered Set: Proof of Reflexive & Transitive under Relation

Trying to prove the following: A set "A" is called a well ordered set if there is a relation R on A such that R is reflexive, transitive, and for all a,b are elements of A, either aRb or bRa. Prove that the set of the integers is a well-ordered set under the relation less than or equal to. Would I just need to prove th

### Permutation Groups : Inverse and Product

Let alpha = [1 2 3 4 5 6] beta = [1 2 3 4 5 6] [2 1 3 4 6 5] [6 1 2 4 3 5] Compute each of the following: a) alpha^-1 b) alpha beta Please see attached for full question.

### g is a linear combination of f1, f2,...,fn iff g(N) = {0}

Functional Analysis Linear Functionals Vector Space Suppose that Ɛ is a vector space, nЄN, and f1, f2,.

### Probability : Permutations and Probability Distributions

1. You dream of someday winning the lottery (don't we all). You found out about a new lottery where the winning numbers are five different numbers between 1 and 34 inclusive. To win the lottery, you must select the correct 5 numbers in the same order in which they were drawn. According to your calculations, the probability of wi

### Interpretation and Comparison of Combination Permutation

1. This week we were introduced to new terminology and symbols. Please interpret the symbol P(B|A) and explain what is meant by the expression. Why is P(B|A) not the same as P(B)? 2. Consider the formulas: nPr =n!/(n-r)! and nCr = n!/(n-r)!r! a. Given the same values for n and r in each formula, which is the smaller val

### Describe Sets in Words

Describe set in words- B ∩ D

### Sets and counting

Six people are going to travel to Mexico City by car. There are six seats available in the car. In how many different ways can the six people be seated in the car if only three of them can drive?

### Combinations : 'Pick k out of n' Problem

Baskin Robbins serves "31 Flavors" of ice cream. How many different two-scoop ice cream cones are possible if two different flavors are used on each cone and the order of the scoops doesn't matter?* (* Means chocolate on top and vanilla on the bottom is the same as chocolate on the bottom and vanilla on top.)

### Sets : One-to-one Correspondence

A.) Show that the following set is infinite by setting up a one-to-one correspondence between the given set and a proper subset of itself: {8,10,12,14,...} b.) Show that the following set has cardinal N sub o by setting up a one-to-one correspondence between the set of counting numbers and the given set: {5,9,13,17,...}

### Set Operations : Union, Intersection, Complement and Number of Elements

Use the information provided to determine the correct answers U={1,5,10,15,20,25,30} A={1,10,15} B={1,10,20,25} C={5,15,30} a.) A U B b.) C ^ B' (the ^ is supposed to be an upside down U) c.) (A ^ C') U B d.) n(A U B)' E.) use the sets provided to draw a venn diagram illistrating the relationsh

### discussion of its subgroups (normal, sylow, cyclic)

Need a full description of alternating group A(4), discussion of its subgroups (normal, sylow, cyclic), and their interrelationships. Any other details you can think of would be appreciated as well. Thanks

### Sets and Subsets : Number of Elements

If n(S) = 10, n(R "union symbol" s) = 16 and n(R "intersection symbol" S)= 2, then n(R) = ? a. 2 b. 4 c. 6 d. 8 e. none of the above

### A Set D is a Subset of Set C

A set D is a subset of set C provided that? a. every element of C is an element of D b. every element of D is an element of C c. at least one element of C is not an element of D d. at least one element of D is not an element C e. none of the above.

### Combinations-Number of choices

1. Joey is having a party. He has 10 friends, but his mom told him he could only invite 6 of them. How many choices are there if a. there are no restrictions b. there are 2 brothers who will only attend if they can attend together c. there are 2 girls who each will not attend if the other one does