Combinations Definition and 415 Threads

Homework Statement Let C_n Recalling our notation from class, we know that I_0(C_n) = 1 and I_1(C_n) = n. Prove that for k > 1, I_k(C_n)=\left(\frac{n}{k}\right)\left(\stackrel{n-k-1}{k-1}\right) Homework Equations I_k implies number of independent sets of size k C_n implies the cycle with...

Combinations! How many... Homework Statement How many letter combinations with 9 letters are you able to make with following letters : M-A-T-E-M-A-T-I-K? Homework Equations Well its pretty obvious you need to use Combinations. Please explain how you solve this problem, don't write...

Homework Statement Find the number of solutions to the equation x + y + z + t = 16, where x, y, z, and t are: i) odd integers ii) even integers Homework Equations N/A The Attempt at a Solution I know the total number of solutions is 19 choose 3. So I'm thinking I can obtain the...

Can someone explain to me how to do this problem... I am really lost... how many ways can you buy a dozen donuts from an unlimited supply of 5 types of donuts?

A subgroup must be formed, with 4 people being chosen from 3 larger groups. Group A contains 6 people Group B contains 4 people Group C contains 3 people The subgroup of 4 must contain atleast 1 person from each group (A,B,C). How many possible groups are there? Well there are 6...

Hey all, im taking geometry and discrete mathematics at my school. Its a 12 U course. And I am not doing as well as i would like in it. I am at about a 75, annd i want that to be around 85. So I am looking to you guys for some help. If you guys wouldn't mind awnsering a few questions i have...

Question regarding two lenses in combination - the first is a diverging lens with f = -31.5 cm, and the second is a converging lens, 14 cm away, with f = 20.0 cm. The exact question is 'Where will an object at infinity be focused?' (coming in through the diverging lens), and I kind of understand...

Hi, I have some queries that I'm hoping you can help me with. Actually these are probably fairly straight forward for this forum but it's been a long time since I've done any formal math so some help would be appreciated. First query: suppose I have 4 objects: A, B, C and D. I want to know...

Homework Statement Find the equivalent capacitance between points a and b for the group of capcitors connected as shown below. http://img250.imageshack.us/img250/7816/40ha4.th.png Homework Equations Series/Parallel combinations. The Attempt at a Solution I don't get how the...

Hi, just joined this forum, I am an EE undergrad and trying to find a solution to the following assignment, hope somebody here could help or point me in the right direction. Given some resistor values (1.8ohm, 20ohm, 300ohm, 24kohm, 56kohm) I must construct series and parallel combinations...

Surely there's an easier way to do this question than the method given? Q: Two couples and one single person are seated at random in a row of five chairs. What is the probability that neither of the couples sits together in adjacent chairs? A: Yes. Let's call the first couple C and c, the...

Homework Statement There are 6 males and 4 females awaiting to see a teller at a bank. Only 4 people can be served at one time. 1) How many ways can four of the people be picked and served one at a time, if they must include two(2) men and two(2) women? 2) If indeed the four people...

hey , just wondering about gluons : red - anti red red - anti blue red - anti green blue - anti red blue - anti blue blue - anti green green - anti red green - anti blue green - anti green Our common sense tells us there's 9 , but in reality there's 8, how come ? I have already...

Hello everyone, Another example from the book I'm going over and I'm not exactly sure how they got their answer: The game of poker is played with an ordinary deck of cards. Various five-card holdings are given special names. a. how many 5 card poker hands contain two pair? Well I'm...

Hello everyone, another example in the book I'm wanting to make sure I'm seeing how they got their answer correctly. It says: Supppose the group pof 12 consists of 5 men and 7 women. How many 5 person teams contain at most one man? Solution: The set of teams containing at most one man...

Hello everyone im' stuck on this problem. It says: Each symbol in braille code is represened by a rectangular arrangement of six dots. Given that a least 1 dot of the 6 must be raised, how many symbols can be represented in brail? I'm thinking I have to use combinations becuase the...

I remember this from awhile back but can't seem to find any justification. Why is the smallest positive linear combination of two numbers necessarily the GCD of the two numbers?

I'm not sure where to start on this one at all, very confused. I don't want anyone to do the entire problem for me just point me in the right direction. I know how to compute probability from simple random events but this question just confuses the heck out of me :( Question: A labor...

Hi all, I am writing a course for budding engineers. I have been a marine engineer for long. While compiling my course I seem to have hit a roadblock that has made me aware of my ignorance in spite of my experience. I would like some help on this from anyone. I have classified diesel engines...

Linear combinations?? :S Hey, could som1 please explain linear combinations. I copied down the lecture notes but I'm not understanding this example :confused: may hav typo from the note takin Example: Show that each of the vectors w1 = (1, 0), w2= (0, 1) and w3 = (3, 3) are a linear...

i am given C(28,2n)/C(24,2n-4)=225/11 where C are combonations. i am supposed to solve for n. after subbing in n and k and simplifying i get (11*28!)/2n!=(225*24!)/(2n-4)! (i am pretty sure this is correct). i do not seem to be able to continue after that. how do i solve for n?

I am doing some work on high school (Australia) level combinatorics. So I've been taught nCr, nPr, and of course factorial (!). Now I need to apply the combinatorics to probability. There a two questions which I am stuck on. I calcualted that the sample space of all combinations was...

struggling with these problems: 1. determine if the following are: i) collinear: A(0, 3, 2), B(1, 5, 4) and C(3, 9, 8) ii) coplanar: A(1, 4, −5), B(2, 12, −8), C(4, 6, − 4) and D(5, 3, −2) i know that TWO vectors are collinear if it is possible to express one as a scalar multiple of the...

:cry: i need help solving problems involving selecting things. like for example find the number of ways in which a team of 3 men and 2 women can be selected from a group of 6 men and 5 women. im doing a retake of a statistics exam i did v badly in btw. i can't find any good websites about...

hello i need help solving problems involving selecting things. like for example find the number of ways in which a team of 3 men and 2 women can be selected from a group of 6 men and 5 women. :bugeye: i know how to do perms and combs but just don't know how to apply them.:eek: help...

Hi, I really need help with this question 1) the water depth in a harber is 21m at hight tide, and 11m at low tide. One cycle is completed approximatly every 12h. a) find an equation for the water depth as a function of the time, t hours, after low tide b) Draw a graph 48h after low...

One of the class objectives is to give an oral presentation to the professor. This time it has to do with explaining Permutations and Combinations. We have 4 things we need to explain: 1) Permutations / Repetitions are not allowed / Order Matters 2) Combinations / Repetitions are not...

The question is to write the following vectors as a linear combination: c) a vector directed at an angle of 45 degrees with a magnitude of square root of 2. d)a vector directed at an angle of 150 degrees with a magnitude of 6. What I tried to do is to find the scalar quantity with the...

From a deck of 52 cards, the 12 face cards are removed. From these face cards, 4 are chosen. How many combinations that have at least 2 queens are possible? The answer is 201... I can't get here. This is what I did: case1) 4 queens can be chosen C(4,2) ways * 10 cards can be chosen C(10,2)...

Four lattices are selected from 5*4 grid board indicated in the figure above so that they form the corners of a rectangle having sides parallel to the edges of the board. How many different rectangles can be formed in this way? Can anyone give me some clues to answer this question? Thanks:approve:

If 4 letters are selected from the 7 letters of the word "WINDOWS", calculate the number of possible a)combinations. b)arrangemants. I have got the answer but I still don't understand how to calculate it. Thanks.:rolleyes:

A manager has Rs.1000 from which he has to give a bonus to his five employees by following a condition that every employee must get atleast Rs.50 and every employee must be given integral amount of Rupees. in how many ways can he do it? Since them manager has to give Rs.1000 to...

You are taking a test with 10 questions, you only have to answer 7, how many ways are there to do it? 10 x 9 x 8 x 7 x 6 x 5 x 4 ? How many different ways are there to answer the questions if you must answer at least 3 from the first 5 questions? 5 x 4 x 3 x 7 x 6 x 5 x 4 ?

I was thinking that I could solve this with combinations. However, I am unsure of how to use it in this case. If I remember correctly, the combinations are given by: \begin{pmatrix}n \\ r\end{pmatrix}=\frac{n!}{r!\,\left(n-r\right)!} Hmm. Any thoughts on this? Am I on the right track...

Suppose I pick two number from {0,1,2} without replacement and suppose I keep track of which one was drawn first. This is a permutation question. There are 3!/(3-2)! = 6 possible permutations: (0,1) (0,2) (1,0) (1,2) (2,0) (2,1) Of course, if I only care which numbers were choosen, then I...

I have a problem that I'm not aware of how to solve. I know about permutations and combinations, but... Given that the possible values for a are all integers such that 2 \leq a \leq m_{a}, and the possible values for b are all integers such that 2 \leq b \leq m_{b}; how many combinations of...

Having a lot of trouble with a particular problem in the topic of variance. The problem is: "Suppose you are organizing a game where you charge players $2 to roll two dice and then you pay them the difference in scores. What is the variance in your profit from each game? If you are playing a...

If anyone is able to help me with this question regarding introductory Data Management, I would be grateful. Find the sum of all the five digit numbers that can be formed using the digits 1,2,3,4, and 5 without repeating any digit. Thank you! Artermis

I was just wondering how you would prove the following: \sum_{k=0}^{n}\frac{n!}{k!\left(n-k\right)!}=2^{n} Any help is appreciated.

In how many ways can 15 gifts be distributed equally: a) amongst Claire, Alana, and Kalena b) into three parcels of five gifts each For (a) I went _{15} P_{3}/3 = 910 I am 100% certain this is wrong. I also have no idea how to do (b). I would greatly appreciate any help on this...

Does an algorithm exist for generating a particular permutation of a combination? You just input the combination and the position of the permutation and it outputs the permutation.

In springs, when two springs are combined in series why is the total spring constant of the system 1/2k, and when three springs are combined in parallel, why is the total spring constant 3k?

Hi, I just started a course about Statistics and I was wondering if I am doing the following question right. Q: A student enters 2 of 6 positive numbers with "-" signs and 3 of 4 negative numbers with "+" signs. If at some stage, a program chooses 3 distinct numbers from these 10 random...

Is it fair to say combinations are just an application of the counting principle? I already understand that permutations are just an application of fundamental principle and that combinations are just an application of permutations. If it's fair to say that combinations are in fact, just an...

Is it fair to say combinations are just an application of the counting principle? I already understand that permutations are just an application of fundamental principle and that combinations are just an application of permutations. If it's fair to say that combinations are in fact, just an...

I had mono while this unit was being taught so I am havin quite a lot of trouble figurin this homework out. Like this question: How many 6 digit numbers greater than 800 000 can be made from the digits 1, 1, 5, 5, 5, 8? I have absolutly no idea so any help would be appriciated! Thanks!

Ok, given a set: A How many distinct x tuples can be created using a subset of A? Example: |A| = 20 I want to know how many combinations of 7 tuples can be made from that set. Example: If A = {1 .. 20} three such combinations could be: {1, 2}, {3, 4}, {5, 6}, {7, 8}, {9, 10}...

What would be the best way to solve for n if 10Pn = 90? Also, how would you solve this problem: In a student council election, there are 3 candidates for president, 3 for secretary, and 2 for treasurer. Each student may vote for at least one position. How many ways can a ballot be marked...

Hi, I've been scratching around trying to figure out a formula for the following problem and I've got one that I think is correct. Just wondering if anyone can confirm it for certain (like maybe you have it in a textbook or know it well etc). Thanks. Problem : You need to partition n=k*m...

if there is lottery where there are six numbers of 49 drawn and each number is discarded one drawn what are the total combinations. I think it would be 49 choose 6 but that only gives 14 million and I figured it would be higher. can someone verify this? thanks :smile: