Counting Definition and 413 Threads

Homework Statement How many natural numbers are there with the property that they can be expressed as the sum of the cubes of two natural numbers in two different ways. Homework Equations N/A The Attempt at a Solution I don't understand how should i start. :( Can somebody give...

Counting Lists With Repetition Homework Statement How many ways can you create an 8 letter password using A - Z where at most 1 letter repeats? Homework Equations The Attempt at a Solution I'm not sure how to attack this problem but first I thought that A-Z considers 26 letters...

How many ways can you place 8 distinct flags on 3 distinct poles if no pole can be empty.Im not sure how to approach this problem because writing out all the possibilities would take a lot of time So I was thinking it would be something like 8C3 to select the three flags that have to be placed...

Homework Statement There are n distinct balls, and n distinct boxes, and one right order for the boxes to be in. What is the chance that none of the balls are in the correct box. And each ball can go into only one box. Homework Equations The chance that none of the boxes are in the correct, is...

Homework Statement (A) Find and prove a bijection between the set of all functions from [n] to [3] and the set of all integers from 1 to 3n. (B) How many set partitions of [n] into two blocks are there? (C) How many set partitions of [n] into (n-1) blocks are there? (D) How many set partitions...

Find the number of way to place m flags on n distinct poles with at least one flag on each pole if the flags are identical. What if the flags are distinct. For the first part I said that there were n^{m-n} because if you have m flag and you need each pole to have a flag you have m-n flags...

Take 4 pennies and 2 dimes. Now assume that you have no way to distinguish the pennies from each other and no way to distinguish the dimes from each other, but you can tell the difference between a dime and a penny. For each of the following situations, how many different ways can you pull...

Hi everyone, I want to make sure if I solved this problem correctly. Thanks in advance. Homework Statement Rachel invited her friends to dinner. She has 10 friends, but only 6 places to sit them in her (circular) table. a) Count the ways to sit the guests if order is not important. b) If...

What is the total number of bones in rabbit and frog? Can anyone help me to group them all...

Homework Statement "Find the probability of the sum of three rolled die being less than or equal to 9." Given problems like this, my question is: is there some way to find the answer besides writing out all 216 combinations and then counting the ones that equal 9? I feel like there is, but...

How come AI never makes an progress? OK this may be slightly over stated but it has been 50 years since we thought we could make an AI soon and we are no where near an AI.

Say you have a free particle, non relativistic, and you want to calculate the density of states (number of states with energy E-E+dE). In doing that, textbooks apply periodic boundary conditions (PBC) in a box of length L, and they get L to infinity, and in this way the states become countable...

Hi and thank you for reading this. I'm learning to use mathematica and among those things I'm trying to do, is to define a function that can count for me, say, the number of positive zeros less than a given number Z of a familly of function. For exemple, let f_n(x) = sin(x/n) for any...

I've been playing with a computational system that represents numbers in their simple continued fraction form. That is, CF([a0,a1, ... , an]) =a0 + \frac{1}{ a_{1}+\frac{1}{a_{2}+\ddots\frac{1}{a_{n}}} }Considering what types of numbers such a system can represent, the finite CF's correspond to...

Homework Statement Consider a system composed of 2 harmonic oscillators with frequencies w and 2w respectively (w = omega). The total energy of the system is U=q * h_bar * w, where q is a positive negative integer, ie. q = {1, 3, 5, ...}. Write down the number of microstates of the system...

I am examining the conjugacy classes of S_5. I know that two elements in S_5 are conjugate if and only if they have the same structure when expressed as products of irreducible cycles. Thus, the conjugacy classes are [(1 2 3 4 5)], [(1 2 3 4)], [(1 2 3)], [(1 2 3)(4 5)], [(1 2)(3 4)], [(1 2)]...

Hey peeps, I was bored the other day and wanted to paint something, so I started tweaking images in mathematica to make them eaiser to paint/draw and I came across de jong attractors and the following http://flam3.com/flame.pdf" . Basically I immediately remembered I had forgotten most of...

Homework Statement A poker hand conatins 5 cards chosen from a deck of 52. 1. How many hands are possible a. 4 of a kind b.3 of a kind c. flush d. full house e. straight f. straight flush The Attempt at a Solution When i write (5,2) I mean 5 choose 2 . 1. (52,5) a. I have 13...

Hi, I want to understand the meaning of orbifold counting. Could anyone help me? Background: I will begin my third undergraduate year in Physics in September.

Homework Statement 100 hundred people are to be divided into 10 discussion groups with 10 people in each group how many ways can this be done. The Attempt at a Solution So if we think of it as people on a 10 by 10 grid their are 100! ways of populating the grid and then 10! ways or...

Homework Statement A software company uses a 20 character product key that new buyers of their product must use during installation to successfully install the software in their computers. The structure of these product keys is as follows. Repetitions are allowed unless explicitly...

Homework Statement A computer operating system allows files to be named using any combination of uppercase letters (A-Z) and digits (0-9) But the number of characters is at most 4 , And there must be at least 1 letter in each file name. The Attempt at a Solution So I break this up into 4...

Homework Statement Let r be a positive integer. For any number x, let (x)r = x(x-1)(x-2)...(x-r+1) Show that (-1/2)r = (-1)rr!2-2r(2r take r) Homework Equations by "2r take r" I mean what is usually denoted by (n / r) (written like a fraction but without the bar) and is calculated...

Homework Statement social security number is a 9 digit number. the first digit may be 0 a. How many numbers are available b. How many are even c. How many have all of their digits even d. How many read the same forward and backward e. How many have none of their digits equal to...

I am attempting to write a program to do the work for me. I started in the process by hand and it took about an hour to get through the letter a. So I have a folder with many sub-folders and each sub-folder has at least one sub-sub-folder and then in theses many sub-sub-folders are the...

I was tought that a physical measurement must be seen as an irreversible collapse of the wavefunction. I always thought that this is an ill defined statement. But let's assume that some macroscopic system is able to perform this act and that it is part of physical reality. My questions: has...

I stopped posting outside of general discussion when I hit 314 posts. I figured pi was a cool number to stop at and I knew I wasnt going to hit Avagadro's, so why do I now have 618 posts?

Homework Statement ----1. From the digits 0, 1, 2, 3, 4, 5, 6, how many four-digit numbers with distinct digits can be constructed? How many of these are even numbers? ----2. How many integers between 1000 and 9999 inclusive have distinct digits? Of these how many are odd numbers...

Box counting dimension! please help! Hi all, I am working on a problem from Chaos theory, I have to find the box counting dimension of the set {0}U{n^-p} where n is an integer and p>0. I started this problem by considering p=1. So, the set looks like {0,1,1/2,1/3,...}. If I take intervals...

Hello! I'm unsure of how to attack the following problem. It states that F_{3} denotes the set of all functions from {1, 2, 3} to {1, 2, 3}, then asks one to find the number of functions f ∊ F_{3} such that (f ∘ f)(1) = 3. Simpler questions are clear to me -- I see, for example, that the total...

Homework Statement How many was can 3 identical prizes be awarded to 98 potential winners? Homework Equations The Attempt at a Solution Well. I know that if the prizes were unique, the first prize would have 98 possible winners, the second prize would have 97 possible winners...

I need help with this math problem: Show that the set of rational numbers, Q, is countable. and Show that the set of irrational numbers is uncountable.

Hello I am new in string theory and I am wrestling with a paper in Beltrami parametrization. Although I have spend time studying ghosts, brs symmetry etc my knowledge in differential geometry is very limited (for string theory). My question is how do I count practically the grading of an object...

The guiding premise of this thread is the following proposition: If fractals play a role in the behavior of partitions, then maybe, just maybe, they play a role also in the positioning of the primes; and if they do, then who is to say that the two, prime numbers and partition numbers, cannot at...

I don't remember any probability from high school which was over nine years ago. This semester I'm taking Thermal Physics and Probability. So, I'm having to catch up with counting techniques and so forth and make sense of the logic behind the techniques...

Homework Statement Either People of different heights are to be seated in a row. The shortest and tallest in this group are not seated at either end. What is the probability that: a) the tallest and shortest persons are sitting next to each other? (Ans: 1/3) b) there is one person sitting...

Suppose an ant is on a vertex of a cube. On one of the three vertices neighboring the ant, there is a black hole. On each move, the ant travels to one of it's neighboring vertices, being careful not to pass through the black hole. The ant makes N moves in total. How many different paths lead the...

what is "counting rate"? Homework Statement Is "counting rate" the same as "rate of decay"? This problem asks about counting rate, but i can't see this term anywhere in my physics book.. Is it like an alternate term for "rate of decay" (also, counting rate isn't even on wikipedia)...

Hello all, I am in a circuits class now and we are doing our end of the year project. I have decided that I want to do some sort of circuit that counts things. For the actually counting portion of the circuit I am just busting open a cheap little calculator and connecting two leads to the =...

Hi all. If I read in variables entered by the user, how can I check to make sure the correct number of variables were entered? For example, after reading in a data file and making it into an array, I have: echo "To check the data, enter the first element number, last element number and...

Hi all, Entropy uses the 6N dimensional phase space. But ... Roger Balian in "Scientific American" takes one liter gas in a cube and he writes: I can replace the continuous volume by Q = 10^100 sites after having evacuated the speeds (he says this is possible with quantum mechanics) He...

I'm working through Srednicki's QFT text, and I'm continuously vexed by the various numerical factors in diagrams and vertices, as well as the grouping of diagrams. For example, in Chapter 10 (pg 75) Srednicki treats basic \phi\phi\rightarrow\phi\phi scattering processes in \phi^3. He claims...

Hi everyone, I have trouble depicting the difference between these two problems. The first problem uses the multiplication rule to solve while the second problem uses the counting rules (combination) to solve. To me, it seems like both problems could be solved using the multiplication rule so I...

Hello all, I am going through some sample problems exercises in Paul Sally's Tools of the Trade, and am being asked to prove the Fundamental Counting Principle. That is, If A has m elements and B has n elements, then A X B has mn elements. Sally goes on to write that "this is simple to prove...

Homework Statement A license plate has three letters followed by three numbers. Suppose the digits from 0...9 can be used, except all three digits cannot be zero, and that any letter from A-Z with repeats can be used. How many plates are possible? Homework Equations My question is on...

Homework Statement A football team consists of 20 offensive and 20 defensive players. The players are to be paired to form roommates. They are paired at random. What is the probability that there are exactly 4 offensive/defensive pairs. Homework Equations The Attempt at a...

*******************I am sorry about this, Please Use My other post Homework Statement A football team consists of 20 offensive and 20 defensive players. Th players are to be paired to form roommates. They are paired at random. What is the probability that...

Hi, I have a question about counting (how difficult should that be ;) ) I have the set of tensors in D dimensions \{h_{\mu\nu}, H^{\mu\nu}, t_{\mu}, T^{\mu}\} with the relations H^{\mu\nu} h_{\nu\rho} = \delta^{\mu}_{\rho} - T^{\mu}t_{\rho} T^{\mu}t_{\mu} = 1...

Homework Statement How many different bit strings can be formed using six 1s and eight 0s? Homework Equations C(n,r) = n!/(r!*(n-r)!) The Attempt at a Solution since there's six 1s and eight 0s there are 14 slots. So I'm guessing for the possible six 1s it would be C(14,6)...

nvm i got it