Combinations Definition and 401 Threads

The total number of different combinations of one or more letters which can be made from the letters of the word MISSISSIPPI is? First i don't understand what the question means and second my answer is completely different from that in my book My working- since there are 11 letter 4 I 4 S 2 P...

Hi, I read that linear combinations of a state, Psi, can be as: \begin{equation} \Psi = \alpha \psi + \beta \psi \end{equation} where ##\alpha## and ##\beta## are arbitrary constants. Can however this be a valid linear combination?\begin{equation} \Psi = \alpha \psi \times \beta \psi...

Hi All, I'm studying for the GRE, and really struggling with combination questions for some reason. I'm posting here quite a bit, but just wanted to say thank you so much for your help. What would be the fastest way to solve the following? "At Deb's Deli, a customer may choose either a...

"Jacob needs to create a 6-digit code for his bank account using the digits from 0 to 9. He wants the first digit to be odd and the last digit to be even. If he does not repeat any digits, how many different 6-digit codes could Jacob create?" Would the best way to solve this be: (5)(9)(8)(7)(6)(4)?

Hello! What is the fastest way to solve the following (I'm prepping for GRE and going too slow right now):"An appliances model number has three alphanumeric characters. The first character must be one of 24 permissible letters in the alphabet. The next character is numeric, a digit from 1 to 9...

Homework Statement On a phone keypad, many of the numbers have letters associated with them. For instance, the letters A, B, and C are associated with the number 2. Write a program that accepts a number as input and prints all of the possible letter combinations associated with that number. For...

Homework Statement There are 22 students in a class. The professor will divide the class into 4 groups. Group 1 and 2 have 5 members each whilst Group 3 and 4 have 6. Given that the teacher forms the group at random, find the probabilities of : A = event where Paula, Trina, Gia all belong in...

HELP! given p(q(x))=2/(5+x) and q(x)=1+x . find a formula for p(x). Someone please help. I don't know how to do this problem .Thanks in advance (PS: would be really helpful if solution is also given)

I have attached an image showing a (what I believe to be) simple problem involving arranging four blocks, each of different dimensions. Yes, the blocks fit together perfectly in the first arrangement shown in the diagram when there are no gaps. I'm convinced that the solution is likely easily...

Homework Statement Homework EquationsThe Attempt at a Solution the answer for no adjoining _W_W_W_W_W_ for 3 red balls, there are 6 positions so ## 6C_3 = 20## i'm curious, on other way to find arrangement? for adjoining = all arrangement - adjoining all arrangement = 3 red can get to any...

Homework Statement In how many ways can 2 females and 3 males be selected from a class of 30 with 20 female and 10 male students? Homework EquationsThe Attempt at a Solution I saw this as a two step process. Step 1 being I have N1 ways of choosing 2 females and step 2 N2 ways of choosing 3...

Homework Statement Hello, I have to solve a problem to calculate all the possible combinations in a dataset. I have candles and each one has 4 values: open, close, high and low. And I have a high number of candles (hundreds). I want to know all the possible scenarios that it's possible to...

Hello, just a quick question. I am aware that a a state in a space can be written as a linear combination of the basis kets of that space ψ = ∑ai[ψi] where ai are coefficients and [ψi] are the basis vectors. I was just wondering is this a linear superposition of states or just a linear...

My 10 year old daughter was given this maths puzzle and I'm sure to you guys it would be pretty easy. You have 5 numbers 1,2,3,4,5 Ho many possible combinations are there possibe for 1 digit combos,2 digit combos, 3 digit combos, 4 digit combos, and 5 digit combos. The numbers cannot repeat at...

Homework Statement Hi everybody! I know, it's a strange question... Problem is that I'm searching how to translate the german words "stromrichtig" and "spannungsrichtig" ("current correct" and "voltage correct" literally) in English. Any idea? Do they even have a name in English? And if not...

Is there an easy way to do this?

Homework Statement A club has only 8 women and 6 men as members. A team of 3 is to be chosen to represent the club. In how many ways can this be done if there is to be at least one woman on the team. Homework EquationsThe Attempt at a Solution I can do this 2 ways, first 1w2m + 2w1m + 3m0m...

Ok, so the problem is: There are 5 letters, ABCDE. How many unique combinations of 3 letters can be made if letter A must be part of the combinations? The solution is that because A must be one of the letters, that only leaves two other letters which you can manipulate. So the answer is...

According to Pauli principle the two fermions can not occupy one state of a Hamiltonian. Can the two fermions occupy a state which is linear recombination of two states of the Hamiltonian?

of size N into an K subgroups. I've been trying for hours to do this and still haven't found a solution. Example: The array {A,B,C} of size N=3 and I want all the move combinations that make it into K=1 subgroups. The only such subgroup is the one with all the elements, and I can get that with...

Hello, I face problems sometimes in identifying the maths of permutation and combination.Can anyone please tell me an easy way to identify quickly whether the math is about permutation or combination? Thank you, Shafia.

Homework Statement 8 friends are playing a tennis game together. How many different doubles games of tennis can they play? Homework Equations Combinations The Attempt at a Solution Well, I solved this problem by saying: we choose a group 4 people from 8 to play, so order is not important...

Hi, I'm a mom trying to help my son understand why he got answers wrong on his online math program. He is taking Geometry, but the last unit in the class is an introduction to Probability and Statistics. After re-reviewing the lesson and re-working the problems he got wrong, we were able to...

Homework Statement What is the probability of choosing 1 Jack from a card deck and then one heart (no replacement)? Homework Equations None come to mind. The Attempt at a Solution I was thinking ##(4C1)/(52C1)\cdot(13C1)/(51C1)## but what happens if the jack drawn is a heart? Do I make cases...

Could anyone give me a help with this combinatorics problem: On a tournament of ping-pong there are 8 contestants and these rules apply: -Every player plays every other exactly once. -If in the i-th round there was a match between A and B and a match between C and D, and in the i+1-st round...

Can someone explain the difference using concrete examples. I will attempt to explain my current understanding by example; A H atom has different energy levels which can be exactly described by algebraic functions with quantum numbers n, l etc. An electron can be excited from say the ground...

If there was a 1 billion x 1 billion x 1 billion cube made of 3D pixel cubes, and half of them are black and half of them are clear/colorless, then how many combinations of unique pixel arrangements are there? Would the amount of shapes/objects in this cube be infinite? (Assuming the black...

We have a square grid. In how many ways we get to the point [20,30], if we can not get points [5,5], [15,10] [15,10] [17,23]? The starting point is [0,0], we can only move up and to the right. Thanks My solutions: $$ \binom{50}{20} - \binom{10}{5}\binom{40}{15} - \binom{25}{10}\binom{25}{10}...

Homework Statement In the xy-plane mark all nine of these linear combinations: ## α \lbrack 2, 1 \rbrack + β \lbrack 0, 1 \rbrack## with c = 0, 1, 2 and d = 0, 1, 2 Homework Equations ANSWER: The nine combinations will lie on a lattice. If we took all whole numbers c and d, the lattice...

Can you suggest any book for learning multinomial theorem and its application in permutation and combinations problems? I am also looking for a book for learning Permutations and Combinations. (Right now, I am using a problem oriented book by Marcus. But I want a book for learning the basics as...

let $f(x)=ax^2+bx+c,with \,\, a\neq 0$ here $a,b,c\in Z$ if the solutions of $ax^2+bx+c=0,\,\, also \,\, \in Z$ given :$f(8)=1$ please find all combinations of $a,b,c$

$m,n\in N ,n<m $ given : $(1)1000\leq m<2011$ $(2) m-n=p^k$ here $p$ is a prime, and $k$$\in\{0,1,2\}$ $(3)m\times n $ is a perfect square number , find all possibe $m$

Hi! If I have points A and B in a lattice in the plane, and the closest path between them is n + m steps (for example 4 steps upwards and 5 steps to the right), there are C(9,(5-4)) = 9 combinations of paths between them. I have to choose the 4 ways upwards (or the 5 ways to the right) of the 9...

I'm working on a project and I need to know how many possible combinations of 16 whole numbers there are that have a sum of 240 or less. How would I achieve this sort of thing?

Hi, I am trying to find the solution (formula) for doing the following: For any number of players (divisible by three), I need to calculate a number of rounds (in my case 8) for three players to play each other without any repetition. So the first round of etc. 21 players would be: 1,2,3 4,5,6...

Hello, I am having trouble understanding the answer to the above question. The answer is 6!/3! and below is my working. I am having trouble arriving at the above answer and here is my approach. The question is to find the permutations of KEEPER minus all the duplicates. Therefore, to count...

Prove that if n is even and r is odd then $$\binom{n}{r}$$ is even. Solution: I know I have these two equalities $$\binom{n}{r} = \binom{n-1}{r-1} + \binom{n-1}{r}=\frac{n(n-1)...(n-r+1)}{r!}$$ Now if n is even and r is odd then (n-r+1) is even. So it seems that we will have at least one more...

I want to get better at this topic and I have trouble finding good questions apart from past year exam questions. I am currently an A- Level student, so can someone recommend me a good book full of challenging questions at my level? To give you some idea of the types of questions in the exam...

I was looking at the attached picture, where it gives the Higgs Mass obtained from the two different channels from ATLAS and CMS. Let's only talk about the diphoton channel : H\rightarrow \gamma \gamma From the ATLAS the mass value is: m_{Ah} =126.02 \pm 0.51 and the CMS: m_{Ch} =124.70 \pm...

How do I find all the different combinations of the point (x,y,z) when x,y, and z can be either positive and negative? For example, what I'm trying to solve is (+,+,+), (+,+,-), (+,-,-), etc. How do I find out how many different points there are and the sign of each variable for each distinct...

Homework Statement Out of 7 women and 4 men you need to choose delegation. On how many ways you can choose delegation that consist of: a) five people - 3 women and 2 men b)any number of people, but with equal number of men and women c) five people with at least 3 women d) five peope where one...

So i have the following: [a b; c d] = [e f ; g h] * [p q ; r s] I have to show that the if the original matrices are written as A = EP then the columns of A are linear combinations of E. I was able to prove [a;c] = p[e;g] + r[f;h] and the same for [b;d] but i don't know where to go from here...

Homework Statement The question is attached in the jpeg file. Homework Equations 1/do + 1/di = 1/f The Attempt at a Solution First reflection : 1/100 + 1/di = 1/80 , di = 400cm ( To the right of the lens ) This means that the image created is a virtual image since it is behind the lens. So...

Hi, I am new here hoping to find someone who can help. I am an artist working mainly in Geometric forms. My work follows a set grid and I want to use math to work out all the possible combinations of my grid. Math generally makes my head hurt, so I am hoping someone can explain in real simple...

Homework Statement Let A be an m \hspace{1 mm} x \hspace{1 mm} n matrix, and let \vec{b} be a vector in \mathbb{R}^{m} . Suppose that \vec{b} is a linear combination of the columns of A. Then the columns of A span \mathbb{R}^{m} Homework EquationsThe Attempt at a Solution I said that...

Homework Statement Consider a 11 digit positive integer formed by the digits 1,0 or both. The probability that no two zeros are adjacent is: Homework Equations None The Attempt at a Solution First digit has to be 1. Total number of permutations=210 Now 1XXXXXXXXXX is the format. Taking 10...

I am unsure about which/what formulas to use for these word problems.. Here is one: How many different 7-place license plates are possible if the first 2 places are for letters 26 letters) and the other 5 places are for numbers (0-9, 10 numbers in total)? Any guidance/help would be greatly...

Having problems with question 9 and what I came up was Case 1: 1st person gets 1 And 2nd person gets 3 OR Case 2: 1st person gets 3 And 2nd person gets 1 OR Case 3 They both get 2 And seeing that they are both dependent events so that once a person receives an article it affects the...

Hi everyone this is my first post. Please let me know if I am not following the proper etiquette. I am helping out a friend with a problem. My answer to part (b) does not match the solution my friend has been given. Four people are selected from a committee of 12 represent the committee at a...

Homework Statement Assuming 10 people pick a number between 1-120 and no two numbers can be the same, how many combinations of numbers can their be?Homework Equations C=N^s The Attempt at a Solution So I know the total possible for 120 would be just 120^10, but if I want to solve for the...