Explore BrainMass


Combinations Application Word Problem

A person has 3 different letters to write, 2 interviews to do, and 2 commercials to review. In making aschedule, (first, second, etc.) how many different combinations are there?

Random walk

Hi I would appreciate if you could help me with this question. Is the question below TRUE or FALSE and explain why ? Question: I have two random walks, both starting at 0 and with a reflecting boundary at 0. Each Step, Walk A goes up 1 with probability 1/2 and down 1 with probability 1/2(except at the boundary). Each

Word problem - A person has 14 close friends.

A person has 14 close friends. (a) Suppose that two of her friends (of the 14 of either gender) do not like each other. If one of the two is invited, the other will not come to the party. How many ways are there to invite 8 people to the party. Explain. (b) Suppose that two of her friends are a couple. She cannot in

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)

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 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 : 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 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?

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

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,...}

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

Combinations in Committees and Groups

5. In how many ways can a man divide 7 gifts among his 3 children if the eldest is to receive 3 gifts and the others 2 each? 6. From a group of n people, suppose that we want to choose a committee of k, k <= n, one of whom is to be designated as a chairperson. (a) By focusing first on the choice of the committee and then

Permutations and Combinations of Committees

We wish to form a committee of 7 people chosen from 5 democrats, 4 republicans, and 6 independents. The committee will contain 2 democrats, 2 republicans, and 3 independents. In how many ways can we choose the committee?

Permutation Groups : Cycles

Here's my problem: Let (i1, i2, . . . , ik) be a k-cycle (k less or equal to n) element of Sn and let sigma be an element of Sn. (i) Find a precise expression for sigma * (i1, i2, . . . , ik)* sigma-inverse. Hint: experiment a little, perhaps, then take a guess and prove it. (ii) Describe precisely the set {sigma * (1,

Permutation Groups - Rigid Motion of a Cube

A rigid motion of a cube can be thought of either as a permutation of its 8 vertices or as a permutation of its 6 sides. Find a rigid motion of a cube that has order 3, and express the permutation that represents it in both ways, as a permutation on 8 elements and as a permutation on 6 elements.

Important Information about Counting

Eight people are attending a seminar in a room with eight chairs. In the middle of the seminar, there is a break and everyone leaves the room. a) In how many ways can the group sit down after the break so that no-one is in the same chair as before? b) In how many ways can the group sit down after the break so that exactly

Introductory probability, basic combination/permutation

There is a lottery in which 2000 individuals enter, and of these a set of 120 names will be randomly selected. Assume that both you and your friend are entered in the lottery. a. In how many ways can 120 names be randomly selected from the 2000 in the drawing? b. In how many ways can the drawing be done in such a way that