Combinations Definition and 401 Threads

fragments of film I read a book called the "Holographic Universe". It explained how a hologram is generated. One aspect of hologram creation holds a puzzle that the book I read did not know the answer to. I have not found the answer anywhere and I am looking for a solution to this puzzle. The...

Homework Statement Given a standard chess board consisting of 64 squares with each game taking a total of 40 moves. Calculate the total number of games which can be played. You are to assume a stalemate situation occurring on the 40th move a completed game.The Attempt at a Solution So there are...

Hey folks, I believe this is the correct thread for this topic. I was debating between general mathematics and statistics. I believe it falls here. So, I play the card game Magic: The Gathering, and one of the core tenants of the game is building a deck from a large variety of cards. The deck...

Homework Statement f(x)= \frac{1}{x} g(x)=2√x Find (f+g)(x) Homework Equations Sorry, first post in the homework help section. What do I put here? The Attempt at a Solution I feel like I'm missing something obvious here. (f+g)(x)=\frac{1}{x} + 2√x =x(\frac{1}{x} + 2√x) = 1 + 2x√x = 1 +...

I am slightly confused on how do we calculate vacuum expectation values of product of creation and annihilation operators for bosons, e.g. ##\langle 0| a_{k_1} a^\dagger_{k_2} a_{k_3} a^\dagger_{k_4} |0 \rangle## If i commute ##k_3## and ##k_4##: $$\langle 0| a_{k_1} a^\dagger_{k_2}...

Given n numbers x1,x2...xn belong to N. x1+x2+x3...xn=m How many different combinations of x1,x2,x3...xn are there?Is there any formula useful here? Note:x1,x2,x3... need not be distinct and also can be 0. Thanks

Hi all, Saw this problem and was wondering if there was a simpler way to do this besides listing out the possible combinations. In a game, each token has one possible value: 1, 5, or 10. How many different combinations of these tokens will give us a total sum of 17?

Homework Statement Prove the following: \frac{n!}{m!(n-m)!} = \frac{n!}{(m-2)!(n-m + 2)!} + 2* \frac{(n-1)!}{(m-1)!(n-m)!} + \frac{(n-2)!}{(m-2)!(n-m)!} The Attempt at a Solution I tried writing following \frac{n!}{m!(n-m)!} = \frac{n!}{m!(n-m)!}(\frac{m(m-1)}{(n-m + 2)(n-m +...

[SIZE="3"]Is there any formula which gives the combinations for n things (taken r at a time, r being less than n) which are NOT ALL different? Say you have a total of n things and in those n things you have p things identical. Then you are required to select r things (r may be less or greater...

This may be simple but I want to see a formula and admit I've been out of school too long to figure this one out. Although it's bugging me! I would like to see a formula, too, not just the answer. So you have 6 items. For example ABCDEF. You must use at least one item. Order does not matter...

Do you have favorite/most handy hotkeys? I started to appreciate them when in class taking notes fast and I don't have a mouse and resent using a mouse-pad heavily. All time favorite for me is "Windows + D". It minimizes all windows and takes you to your desktop. Absolutely love it. Close...

Hey guys, I have a problem relating to combinations and permutations.In how many ways can I divide a deck of 52 cards into piles of 3 with each pile containing any number? for example 50,1,1 or 45,6,1 Thanks in advance

First of all, I'm not strong in math, but always interested in learning more. This is an "intellectual satisfaction" type of question, meaning knowing the answer won't really impact anything, but will afford me a certain satisfaction by quenching my curiosity. Maybe someone out there would be...

Homework Statement Construct a matrix whose nullspace consists of all combinations of (2,2,1,0) and (3,1,0,1). Apparently, the answer is: http://www.wolframalpha.com/input/?i=%7B%7B1%2C0%2C-2%2C-3%7D%2C%7B0%2C1%2C-2%2C-1%7D%7D Homework Equations Ax = b (where x and b are vectors and A...

Probability Question -- using the combinations counting form C(n,k) Homework Statement 4. A bowl contains 3 red chips, 4 green chips, and 5 blue chips. A batch of 3 chips is withdrawn at random. (a) What is the probability that the batch contains only red chips? (b) What is the probability...

Homework Statement A large Box of biscuits contains nine different varieties. In how many ways can four biscuits be chosen if : a)Two are the same and the others different b)Two each of two varieties are selected c)three are the same and the fourth is differentHomework Equations Combinations...

An office furniture manufacturer that makes modular storage files offer its customers two choices for the base and four choices for the top, and the modular storage files come in five different heights. The customer may choose any combination of the five different-sized modules so that the...

When the book says "Members of [[S]] are linear combinations of linear combinations of members of S". [S] basically means the span of the members in subspace S. Since [S] = {c1s1 +...
+ cnsn|c1...cnεR and s1...snεS} what does [[S]] mean? does it mean a linear combination of atleast one linear...

Homework Statement 6. a) In your pocket you have some nickels, dimes, and quarters. There are 20 coins altogether and exactly twice as many dimes as nickels. The total value of the coins is $3.00. Find the number of coins of each type. b) Find all possible combinations of 20 coins...

This is similar to one of my previous posts, but is quite different. There are 13 buttons (numbered 1, 2, 3, ...13)in this combination lock, and you have to figure out which ones can be pressed in. They can either be pushed in or left into their original extended position. You don't know...

Hello, I heard a scientist on the radio claiming that, if the universe is infinite, that all possible combinations of matter/energy exist somewhere in that infinite-ness. So, for example, as I sit typing, I am wearing a gray sweater. As I understand it, somewhere in the infinite universe I...

I have two basic questions about combinations. If there are e.g. 10 objects of which 3 are identical and you want to pick a group of 6 out of those 10, how many groups could you get in this case? I know how basic combinations work, but what if there are identical objects involved? And my...

Homework Statement In a polygon , no three diagonals are concurrent. If the total number of points of intersection of diagonals interior to the polygon be 70 , then find the number of diagonals of the polygon. (You must get a numerical value..) Homework Equations Number of diagonals...

Consider an m x n table containing single digits 0 to 9. So each cell contain the digits 0 to 9. My goal is to make sure that all combinations from 000 to 999 can be found in the table in adjacent cells. A cell is adjacent to the cells around it (i.e. above, below, to the left, to the right...

This is not a homework problem but in fact a solved example question. The full question text is below with answers and my reasoning for them. Could someone please explain the reasoning behind part (c). A coffee shop sells 5 types of coffee (latte, mocha, espresso, cappuccino and iced...

Posts: 10 I am a woodworker, and am designing a two part magnetic/spring lock for my blanket chest. The first part has 3 master buttons (primary buttons A, B, C), and the second part has 11 secondary buttons (1, 2, 3, ...11). What you do first is choose 1 of the 3 master buttons that opens...

Ok give me a break, this is my first lesson in my new linear algebra book. Seems fairly straightforward but a little befuddled as to whether I am doing this. The question states "Describe geometrically (line, plane, or all of R^3) all linear combinations of..." Then I have a matrix v = [1 2 3] w...

I was wondering how they got all the different combinations of points? Why can't they just put (+-√2,+-1,+-√(2/3)) ?

Hi all I am new , and wanted to ask the following. I do not know if this is the right section but here goes: I have three registers , say A , B and C Case 1:A will always have 3 combinations 1,2,3 1 has further subsections 1_1,1_2,1_3,1_4,1_5 2 has further subsections 2_1,2_2,2_3 3...

Hello, Quick question, not really homework but more of a general inquiry. Take three vectors: a,b and c such that a and c are orthogonal. Is it possible to write c as a linear combination of a and b such that: c = ma + nb where m,n are scalars. I was thinking not at first glance but...

EDITED: Should be permutations not combinations Homework Statement You have a bag of 10 marbles. There are 4 red marbles, 3 yellow, 2 green, and 1 blue marble. You remove them from the bag one of the time without replacement. Assuming each color of marble is identical and it doesn't matter...

I cannot visualize the geometry for either of these ideas. Is it the case that two vectors can be linearly independent or dependent of each other? In which case, what is the dependency or independency based on? What are these two vectors independent or dependent of with respect to each other?

Lets say you have 3 vectors v1, v2,v3. They form a 3x3 matrix. Let's say you're asked if v3 is a linear combo of the other two vectors. Rref of the matrix gives 1 0 1 0 1 0 0 0 0 The definition of a Linear combo is v3=c1v1+c2v2 where c1 and c2 are scalars. Okay do this is where...

Homework Statement Determine if b is a linear combination of a1, a2, and a3. a1= [1,-2, 0] a2 = [0, 1, 2] a3 = [5, -6 8] b= [2, -1, 6] The Attempt at a Solution Alright, well I used an augmented matrix to solve the problem, and after reducing it completely, the matrix looked...

This is born out of musings around coalition governments that arise from the party with the most votes not achieving ≥50% of the votes (as opposed to emergency coalitions). Taking the figures below how would one go about determining all the possible combinations of parties who combined have...

Hey, so i think this is a fairly simple question but i'd like to get it firmly understood in my head. How do you figure out the amount of combinations of digits in say a 4 digit code. with numbers 0-9... I can't think of a good way to say it, but for example you could have 0,1,2,3 or...

Homework Statement Represent the following combination of units in the correct SI form using the appropriate prefix km*mN Homework Equations k = 10^3 m = 10^-3 The Attempt at a Solution km * mN = (10^3)m * (10^-3)N = m*N = Nm Have I done this correctly?

Homework Statement Let n, k be in the set of all positive integers including zero. Define (n k)=n!/k!(n-k)! Determine the value of \sum (n k) from k=0 to n. Determine the value of \sum (n k) from k=0 to n. The Attempt at a Solution I tried evaluating for some n value: (n 0)= 1 (n 1)=...

I'm not sure if this is the correct place to ask this question, so please let me know if there is a better place for me to post it. I'm having trouble understanding index notation. I understand the basics, such as in the following examples: (a x b) = εijkajbk εijkεiab = δjaδkbδjbδka...

1. how many combinations are possible with the four quantum numbers? 2. Does Pauli's exclusion principle apply only to electrons within the same atom? can it apply across atoms as well? how is the exclusion principle generalized across atoms?

Homework Statement There are N villages which have to be connected using one-way roads in a manner that for every two villages there exists at least one route to travel from one to another. How many different solutions are there? Homework Equations This fits pretty well not only into...

Hi, I am searching for a smart way of calculating all numbers in a special matrix kind of game. The game board consist of numbers between 1 and 9 in a 4x4 matrix. Swiping over numbers will either add up (swiping left or right), subtract (swiping up or down) or do nothing (diagonal...

Homework Statement I'm a little weary of posting this in this forum. If I post it in the math section it will be answered in about 30 min whereas here it might take about 5 hours, but we'll see. Homework Equations The Attempt at a Solution Number one, I'm not exactly sure how they get from...

Hi all, I have a set of questions, with answers in brackets at the end of each of them. I really don't know how to solve them, and have spent a whole morning trying to figure them out. Please help me! (answer one/all of them!) 1. In a game of chance, each player throws two unbiased dice and...

Hi, I have a terrible time understanding one of the concepts in the following question: How many 7 persons committees consisting of 4 females and 3 males may be assembled from a pool of 17 females and 12 males. Ok, so I get this is a combination question. Splitting this between male...

I'm loosely familiar with the formulas for combinations and permutations. However, I don't know how to use the formula with restraints. Here is the specific issue I am having: Number of Objects: 16 Number of States: 2 Number of Black Objects 8 Number of White Objects: 8 How many unique...

1) What is mean by fermion with half integer spin and boson with integer spin Is that fermion, 1/2,3/2... boson, 1,2,3 2) Why meson don't have q = +1, S = -1 or q = -1, S = +1 in term of quark model

Hello everyone, I'm new to the forum and have an engineering problem I've been trying to solve for my job. The actual problem is rather hard to describe but it can best be explained with the following analogous scenario. Suppose I had a bag containing 3 red, 2 blue, and 1 green marbles...

there are 4 circles and 4 straight lines...find the maximum number of intersecting points possible in the intersection of all these given figures...i can't get how to solve it...

Hi. I need a little help. I'm trying to work out how many combinations of characters there are for a string that is between 1 and 8 characters long and uses a-z (non caps) and 0-9. There are 36 useable characters and the string could be anything from simply 'a' to '99999999'. I was able to...