Combinations Definition and 401 Threads

Hello! Christina, thank you for this thread. I also have the same issue. I like Serena, I would be grateful for your further help. If given vectors are (1,2,3) and (3,6,9) that have v3 = v1+v2, does it mean that the whole V vector or W vector lies only on XOY plane (two dimensional) and OZ is...

Homework Statement Is it true that for each ##n\geq 2## there are two primes ##p, q \neq 1## that divide every ##\binom{n}{k}## for ##1\leq k\leq n-1##?Examples: For ##n=6: \binom{6}{1}=6; \binom{6}{2}=15; \binom{6}{3}=20; \binom{6}{4}=15; \binom{6}{5}=6.## So we can have ##p=2## and...

We're currently studying counting and the different equations which are the foundation of probability (permutations and combinations). I understand that permutations are used when order is taken into account and combinations is for when order doesn't matter. However, the two equations appear...

I was going through a p and c problem where I had to find the number of non congruent RECTANGLES. Answer includes number of squares as well. SHOULD SQUARE BE TAKEN AS A RECTANGLE?

Can someone please explain the following question? I am also posting the solution but I didn't understand it well enough. Why is the answer (C)? Can someone explain it to me?In a shooting competition, three targets are set as shown : Condition : Target (I) has four rings on which a person...

Homework Statement Let there be exactly n elements in X and exactly m elements in Y. How many different functions f: X -> Y can we form? How many different injections, surjections (and bijections for that matter)? (There is no further info on m, n.) Homework EquationsThe Attempt at a Solution...

Homework Statement The total number of ways in which 5 balls of different colors can be distributed among 3 persons so that each person gets at least one ball is Ans: 150Homework EquationsThe Attempt at a Solution I don't understand what's wrong with my answer. In case of each person getting...

Hi there all, Big fan of the site and info provided. I stumbled onto it just looking for general info and perhaps some up to date opinions on suspenion for stock clip applications for dirt racing. I have been in the industry for some time, ie; NASCAR fabricator, DIRT chassis builder (NE mods...

Question: ----- Graph all three of f(x), g(x), and the indicated combination on the same axis. In each case, state the domain and range of the composite function. f(x)= (2^-x) , g(x)=sin10x, y=(2^-x)*sin10x ----- THE GRAPH: http://www.wolframalpha.com/input/?i=%282^-x%29sin10x I have a...

Homework Statement Suppose \mathbf{u,v,w} \in {\rm I\!R}^2 are noncollinear points, and let \mathbf{x} \in {\rm I\!R}^2. Show that we can write \mathbf{x} uniquely in the form \mathbf{x} = r\mathbf{u} + s\mathbf{v} + t\mathbf{w}, where r + s + t = 1. Homework Equations Suppose \mathbf{a,b}...

Note, this is not a homework problem, as I'm not even in college. I just had a quick question. I know the formulas to do things such as "How many ways could you choose 5 balls from a tub of yellow, red, and blue colored balls?" (where you envision in this case, a tub where there's more than...

Homework Statement We need to select 5 committee members form a class of 70 students. How many possible samples exists? How many possible samples exists if the committee members all have different roles? Homework Equations nCr = n! / (r!(n-r)!) The Attempt at a Solution I...

Question: You are traveling to South America in two weeks. A friend bought you 5 watches and 6 pairs of sunglasses. You can bring at least 2 watches and at least 1 pair of sunglasses, and can only bring 4 items (so you don't lose all of them). How many combinations of watches and sunglasses can...

Homework Statement Suppose that three computer boards in a production run of forty are defective. A sample of five is to be selected to be checked for defects. a. How many different samples can be chosen? b. How many samples will contain at least one defective board? c. What is the probability...

Hello, How do I solve this problem: In a factory there are 40 employees. A union of 5 people is being chosen. How many combinations are they, if the union of 5 people contains 5 different roles, and an employee can have more than one role (up to 5) ? It is like sampling with replacement, so...

Homework Statement Hi So the problem in combinations is the following: In how many ways can you choose 2 letters from the following 6 letters (A,B,C,D,E,F) This is a question in combinations so I know the order does not matter, so AB is the same as BA. I use the equation (n,r) =...

I thought it would just be the number of faces multiplied by the nine cubes on each face? What am i doing wrong?

Homework Statement In how many ways is it possible to select one or more letters from those in INSIPIDITY? Homework Equations The Attempt at a Solution My initial impression was that this was a combinations problem and I did not have to take into account the repetitions. This led...

I have 16 items and i need to know the number of possible combination for all 16 items. I know the possible number of combination for all 16 items is 1 and the possible number of combinations for 15 of the 16 items is 16 using the formula below: \frac{n!}{r!(n-r)!}. How can i adaprt this...

Homework Statement there are 10 women and 12 men. 5 pairs are to be made, each pair having one man and one women. how many pairings are possible. The Attempt at a Solution first let's choose men and women from each set. there are ##{10 \choose 5}## women and ##{12 \choose 5}## men. now that we...

The scores X1 and X2 in papers 1 and 2 of an examination are normally distributed with means 24.3 and 31.2 respectively and standard deviations 3.5 and 3.1 respectively The final mark for each candidate is found by calculating 2X1+1.5X2. Find the probability that a random sample of 8candiates...

Homework Statement Consider the Parity Operator, P', of a single variable function, defined as P'ψ(x)=P'(-x). Let ψ1=(1+x)/(1+x^2) and ψ2=(1+x)/(1+x^2). I have already shown that these are not eigenfunctions of P'. The question asks me to find what linear combinations, Θ=aψ1+bψ2 are...

Hello everyone, I am an aspiring math teacher taking a workshop type class and in two weeks my group will be teaching the other students various topics on probability. We are trying to come up with a fun and interactive way to teach the counting principle, permutations, and combinations. To...

Here is the problem I have faced recently that I cannot deal with yet and I need some help: Given is the - list of elements (numbered): e.g. [1,2,3,4,6,7,8] - the count and size of groups, which can be used to cover the given set of numbers, e.g. groups with group size 2. - I need to find...

Homework Statement In how many ways can 4 articles be divided between 2 people when each person must receive at least one article? Homework Equations The Attempt at a Solution I tried it like this Person 1 could have ( 3,2 or 1 paper(s) ) Person 2 the same so total # ways...

I am not sure if this is the right sub-forum to post this question in or not, if not I appologize for posting in the wrong place - it looked like the most likely forum to be the correct one. In a sci-fi book I was reading, the author talked about an 'artificial symbiote' being created by 15...

Hello Everyone, Pardon me if the following is incoherent. From what I understood of what my professor said, he was basically saying that when a vector can be written as a linear combination of some vectors in a span, this means, geometrically, that the vector is in the plane that the span of...

I know that someone posted this before, however I could not respond to that thread. I have not taken a Math course in several years and although I can do basic math and algebra, linear algebra is already seeming to be quite difficult. Basically with the title(subject line) the linear...

Hi quick question. I was recently posed a question by a co-worker who saw it in a liquor store contest: 156 different brands of beer for sale You can build your own six pack with any of the 156. How many different ways can you fill the six pack without having the same brand for more than...

Hey there! I will start of with saying I´m not very good at English when considering mathematical terms, neither an expert in Math. My question goes as this: I have a set of 1000 questions - which will be given in rounds with a set of 10. So every round, you get 10 questions out of...

Hello I have the following combinatoric problem : I want to distribute n (equivalent) atoms among M distinct objects. Each object can contain from 0 to nlim atoms. How many combination do I have for this system? If nlim>n, this problem actually corresponds to the classical "Number of...

Reviewing for finals and got this question wrong: How many different permutations are there of the letters in the word LOLLIPOP what I did was 8P8, how would you solve this?

Hello friends, I have problems in simplifying electrical circuits. I've attached 2 (of the many) questions I have trouble with. According to the question, superposition must be used to solve these. In the first question, supposing the voltage source doesn't exist, how do you simplify the left...

Homework Statement Hey everyone I couldn't really fit a good description into the title. Basically here's what it is. Consider an atom in which all the states with principal quantum number n = 3 and angular momentum quantum number l = 2 are occupied by electrons (this is called a closed...

First of all, I would like to apologize for my bad english. The Problem: There is n members inclusive CEO and 2 vice presidents. In how many ways can they be seated around a table so that both vice presidents sits next to the CEO?Attempt at a solution: There's in total (n+2)! ways to be...

When you have combinations where digits are 0,1,2...,m, meaning we have n=m+1 and k, is there a way to see how much of them sum up to a given number? For the sake of simplicity I have the digits 0,1,2...,7 (so n=8), and k=3. I need to find how much of these combinations WITH repetition sum up to...

Hi there, here´s my (unsolved) problem. I´d really appreciate a thorough answer. 10 different persons are to be assigned to 5 different tasks: Every person must have exactly one assignment, and a task can (of course) be assigned to more than one person. A possible combination could be: task...

hey all if i have, say 10 y's, 5 x's, and 4 z's and i want to see how many groups of 6 i can make with at least 5 y's, i know the answer is {10 \choose 5}{9 \choose 1}+{10 \choose 6} which is the combinations of 5 x's added to the combinations of 6 x's. but why isn't the answer {10 \choose...

Hi all. I wanted to double check some of my work, and get some feedback if there's any errors. Any help is appreciated! a) A particular digit (say 5, for example). Essentially we're choosing one digit. 10C1 is 10, and we have 5 slots, so the answer here is 10^5 = 100,000 combinations. b) A...

Hello everyone. Thanks for this amazing forum. I hope I can be forgiven for asking for a software problem rather than a topic specific puzzle. I am looking and happy to pay for a downloadable program I can run from my desk top which will return all possible combinations of numbers for...

Combinations of groups question [edited question] The camera club has 5 members and the mathematics club has 8. There is only one member common to both clubs. In how many ways could a committee of four people be formed with at least one member from each club? I am confused about the "one...

Homework Statement Homework Equations Y=1/2*(X1-X3)^2+1/14*(X2+2X4-3X5)^2The Attempt at a Solution For (a) part, I have only learned to find the moment-generating function of Y, but not finding the p.d.f. Moreover, the examples I have seen only involves random variables Xi to the power 1, but...

Homework Statement Using the values 1, 0, and *(to represent any number), list all the possible combinations that could result from performing reduced row echelon form on a 2 x 3 matrix. Homework Equations Instructor 2 x 2 matrix example: The Attempt at a Solution I have found...

Homework Statement I'm trying to derive the PGF for the Binomial. The Attempt at a Solution I have it whittled down to \sum^{n}_{x=0}(nCx)(\frac{sp}{1-p})^x I just don't know how to simplify this further. Any help is most appreciated.

The title may be incorrect, I named this after the section of my book in which this is located. My problem is as follows. Determine \(\omega_0\), R, and \(\delta\) so as to write the given expression in the form \(u=R\cos(\omega_0 t-\delta)\) \(\color{blue}{u=4\cos(3t)-2\sin(3t)},~\text{My...

Homework Statement How do we derive the total spring constants of different mass spring systems Homework Equations F= kΔx The Attempt at a Solution

Hello everybody. I have a simple combination problem. If I am trying to generalize the number of possible combinations of a nxn block with n objects. So let's say we have n=5. If we have a 5x5 block (25 spaces) with 5 objects (assume objects cannot share spaces), what is the total...

Homework Statement To put it simply, there are 4 different flavors of ice cream, and 6 different toppings. a)how many sundaes are possible using one flavor of ice cream and 3 diff toppings? b)How many sundaes are possible using one flavour of ice cream and from 0 to 6 toppings? c)How many...

I am trying to find all combinations of a four element vector that contains only 1's and -1's. Ex (1,1,1,1),(-1,1,1,1),...(-1,-1,-1,-1) etc My idea to do this is pretty inefficient I am sure but I can't think of another way to do it, so here is what I was trying to do. I found how many total...

Here are the questions: I have posted a link there to this topic so the OP can see my work.