Counting Definition and 392 Threads

how to solve exercise (34) in discrete Math Adv Counting Techniques - see picture===> how apply the formula?

I'm reading these lecture notes but there is something I don't understand. In page 15, it starts to consider vacuum diagrams of various orders and tries to associated a factor to them according to the rule: ## diagram \sim (\frac \lambda N)^p(\frac N \lambda)^v N^l=\lambda^{p-v} N^{l+v-p}##...

More details are yet to come through, but two events have happened in France today which are not good: http://www.stuff.co.nz/world/europe/82135091/live-french-truck-crash-at-bastille-celebrations and http://www.newshub.co.nz/world/eiffel-tower-on-fire-after-explosion-2016071510?ref=newshubFB

Homework Statement How many 3 digit numbers can be formed from 0 to 3 without repition Homework EquationsThe Attempt at a Solution What I did first is H = number of choices for the hundreds place T = number of choices for the tens place U = number of choices for the units digit H = 3...

How many 3 digit even numbers can be formed from 0, 1, 2, 3, 4, 5 and 6 with no repetition? My attempt: $\frac{5}{H} \times \frac{6}{T} \frac{0}{U} = $ 30 numbers ending with zero not including two digit numbers starting with zero$\frac{4}{H} \times \frac{6}{T} \frac{2}{U} = $ 24 numbers...

Hey guys, another question regarding MatLab here. In this assignment, I need to create a function of 'k' to count the number of floating point operations in the algorithm that I've made. Here is my code so far: expAk = zeros(1000, 1000); load('CA3matrix.mat'); times = zeros(15, 1); for j =...

I am having trouble with this program with negativeCntr . Any one explain what i am doing wrong and guide me please. [CODE]#include <iostream> #include <cstdlib> using namespace std; class IntNode { public: IntNode(int dataInit = 0, IntNode* nextLoc = 0); void InsertAfter(IntNode*...

Homework Statement I have two questions. I'm not sure if I'm allowed to post two at once so I'll start with one "Twenty boys and twenty girls are to take a ride on a Ferris wheel with twenty pods. How many ways can they be arranged if each pod is to contain one boy and boy girl" Homework...

Homework Statement Give combinatorial proofs of the identities below. Use the following structure for each proof. First, define an appropriate set S. Next, show that the left side of the equation counts the number of elements in S. Then show that, from another perspective, the right side of the...

Homework Statement 1) We choose randomly 10 persons from 10 dance couples, but we need at least one dance couple. In how many ways is this possible? 2) If we divide n+1 books among n children and every child has to get at least one, in how many ways would this be possible? Homework Equations...

I once heard a mathematician (Adrian Banner of Princeton I believe), say the most natural way to count would be in units of ##e^1##, I've been thinking about this recently and can't think of how this would work, and how it would be more natural. Does anyone have any ideas on where to start?

Homework Statement I have 3 yellow and 7 blue marbles. I put those randomly in a line. What is the probability that no yellow marbles are next to each other? Homework Equations / The Attempt at a Solution Total amount of opportunities to put those marbles next to each other: 120 Total...

Homework Statement Counting problems are a very tough subject to me, so if someone could give me tips, examples explaining what's really happening, that would be great. Homework Equations I know what permutations, variations, combinations, ... are. The problems involving only one of those...

I'm talking about different bases here. I've heard a bunch of people say that base 12 is the best way to go, since it would make basic math easier. After all, 10 from the decimal system has only 4 factors (1,2,5,10), whereas 12 from the duodecimal system has 6 (1,2,3,4,6,12). But, looking from a...

Homework Statement Count the number of surjective functions from {1,2,...,n} to {a,b,c,d}. Use a formula derived from the following four-set venn diagram: Homework Equations None provided. The Attempt at a Solution First, I divided the Venn diagram into sets A,B,C,D and tried to express...

The problem statement: How many five-letter strings of capital letters have a letter repeated twice in a row? For example, include ABCCA and AAABC and ABBCC but not ABCAD. The attempt at a solution: First, let's break down how we would perform the selection of a string that meets the...

Dr Google has failed me, lots of descriptions on how its used but no circuit diagrams and how it works. Seems like a fascinating technique. Anyone got a link to a circuit diagram with explanation. Are these things available as an off the shelf black box type of deal?

Came to know about the following problem from a friend which can be simplified to the following: A1, A2, ...Am and B1, B2,...Bn are two groups of sets each group spanning the sample space. Now there are p elements in each of Ai and each element is in exactly p1 of the sets of the A group. Again...

Homework Statement A box of valentine candy hearts contains 52 hearts of which 19 are white, 10 are tan, 7 are pink, 3 are purple, 5 are yellow, 2 are orange and 6 are green. If you select 9 pieces at random (without replacing any), what is the probability that 3 are white, 2 are tan, 1 is...

Homework Statement I am given a numerical example (to be solved with pen, paper and calculator only) of an RBS spectrum of a AuAgCu-alloy on a glass-substrate. The question is "Can you get the composition? How accurate is the result?Homework Equations All the Rutherford Backscattering...

Write a while loop that prints 1 to userNum, using the variable i. Follow each number (even the last one) by a space. Assume userNum is positive. Ex: userNum = 4 prints: 1 2 3 4 #include <iostream> using namespace std; int main() { int userNum = 0; int i = 0; userNum = 4; //...

Homework Statement Given 9 good light bulbs and 4 defective light bulbs, how many ways can you select 3 such that you get exactly 1 defective bulb? Homework Equations C(n,r) The Attempt at a Solution I understand total ways to select is C(13,3)=286, and that total ways to select only good...

So I'm trying to figure out the best way to count the degeneracy of states for a 3-d particle in a box. The problem breaks into the following: we have three integers greater than or equal to unity whose values are allowed to vary independently, and the sum of whose squares equals a fourth...

Homework Statement A detector is used to count the number of gamma photons emitted by a radioactive source. If the number of counts recorded in exactly 20 seconds is 10000, the error in counting rate per second is (a) 5.0 (b) 22.4 (c) 44.7 (d) 220.0 Homework EquationsThe Attempt at a Solution...

Hello PFers, I'm trying to make a program in java which process user's position, initial velocity of the projectile and the elevation of the projectile and show the trajectory in GUI. The language is in java. The problem is, the trajectory won't show. It is supposed to show the player's...

Homework Statement A bottle of nail polis remover contains approximately 2.5 mol of ethyl acetate (C4H8O2) How many atoms are in the bottle? Homework Equations ? The Attempt at a Solution Would there just be 14 atoms?

Homework Statement 50 students live in a dormitory. The parking lot has the capacity for 30 cars. If each student has a car with probability 12 (independently from other students), what is the probability that there won't be enough parking spaces for all the cars? Homework Equations P(A) =...

The following calculates the number of times the sum of two dice (randomly rolled) equals six or seven. #include <iostream> #include <cstdlib> using namespace std; int main(){ int i = 0; // Loop counter iterates numRolls times int numRolls = 0; // User defined number of rolls int numSixes =...

Homework Statement For reference, this is the image setting up the problem. "A wireless sensor grid consists of 21×11=231 sensor nodes that are located at points (i,j) in the plane such that i∈{0,1,⋯,20} and j∈{0,1,2,⋯,10} as shown in Figure 2.1. The sensor node located at point (0,0) needs...

1) Calculates the number of times the sum of the randomly rolled dice equals each possible value from 2 to 12. 2) Repeatedly asks the user for the number of times to roll the dice, quitting only when the user-entered number is less than 1. Hint: Use a while loop that will execute as long as...

Homework Statement If you have a 52card deck and split it evenly to 4 people (a,b,c,d) then what is the probability that persons a and b have 7 spades and person c has 3 spades. Homework Equations P(A) = |A|/|S| The Attempt at a Solution I divided up the decks 4 ways. So Persons a and b...

Homework Statement An ice cream shop has a special on banana splits, and Xing is taking advantage of it. He’s astounded at all the options he has in constructing his banana split: · He must choose three different flavors of ice cream to place in the asymmetric bowl the banana split is served...

Just for fun, I tried enumerating the topologies on n points, for small n. I found that if the space X consists of 1 point, there is only one topology, and for n = 2, there are four topologies, although two are "isomorphic" in some sense. For n = 3, I I found 26 topologies, of 7 types. For n...

Homework Statement A code consists of at-most two identical letters followed by at-most four identical digits. The code must have atleast one letter and one digit. How many distinct codes can be generated using letters A-Z and digits 1-9. Homework EquationsThe Attempt at a Solution //One...

I've been thinking about the number of degrees of freedom in a tensor with n indices in 2-dimensions which is traceless and symmetric. Initially, there are 2^{n} degrees of freedom. The hypothesis of symmetry provides n!-1 number of conditions of the form: T_{i_{1}, \ldots i_{n}}-...

Hello, I need to learn as much as I can about single photon counting pixel detectors (producing a signal for each photons hitting the detector) e.g. PILATUS. I do not understand how this type of detectors counts single photons as opposed to integrating the energy of multiple photons (CCD, MOS...

A standard 8x8 chess board has but a lone rook in the bottom left corner. A rook a piece than can move any number of spaces either horizontally or vertically. If the rook can only move up and to the right, how many possible paths does it have to the top right corner? I think it's a pretty...

Homework Statement Let A = {1, 2, 3, 4} and let F be the set of all functions from A to A. Let R be the relation on F defined by: For all functions f, g that are elements of F, (f, g) are only elements of R if and only if f(i) = g(i) for some i that is an element of A. Let the functions α, β...

Homework Statement [/B] A stone tossed into a body of water creates a disturbance at the point of impact that lasts for Dt = 4.0s. Measurements indicates that the wave speed is v = 25 cm/s. (a) Over what distance on the surface of water does the wave group extend? (b) An observer counts 12 wave...

Homework Statement Board of directors has 10 members. from the 10 members they will elect 5 officers. President, vice-pres, sec and treas A) From the 10 board members how many combinations of officers are there? B) If three board memebers are physicians, how many combinations have a physician...

Hi guys, So basically I'm trying to find the time ordered product: T(:\phi^{3}(x)::\phi^{3}(y):) for a phi^{3} theory and I'm really having trouble counting the Wick contractions. I've counted the first order contractions which I found to be 9. Second order I got 12 but I don't know if its...

< Mentor Note -- thread moved to HH from the technical forums, so no HH Template is shown >[/color] I have a file Aggregation.dat ######################################################################################## 6.999e+04 4.50000e+01 2.22222e+00 4.94813e+00 2.50000e+01 1.00000e+00...

"For years, telephone area codes in the U.S. and Canada consisted of a sequence of three digits. The first digit was an integer between 2 and 9, the second digit was either 0 or 1, and the third digit was any integer from 1 to 9. (1) How many area codes were possible? (2) How many area codes...

All the youtube links are time stamped 1. Homework Statement Homework EquationsThe Attempt at a Solution I wrote it out the operator expressions each by hand and got the same result but I don't understand how he is able to just eyeball it. I'm trying to develop some intuition. a. To start...

Homework Statement Let F be the set of one-to-one functions from the set ##{1,2,..,n}## to the set ##{1,2,...,m}## where ##m \geq n \geq 1##. Then how many functions f in F satisfy the property ##f(i)<f(j)## for some ##1 \leq i \leq j \leq n## Homework EquationsThe Attempt at a Solution...

Hi 1. Homework Statement On the party came n people. In the beginning all of them have had exactly 3 friends among party members. During party some people made new friends and at the end of the party everyone had exactly 4 friends among party members. Set all numbers n for which the following...

Hi, I came across a question in an exam which I couldn't really relate to any topic of physics, that I had studied. It goes like this- A detector is used to count the number of gamma rays emitted by a radioactive source. If the number of counts recorded in exactly 20 seconds is 10000, the...

we have to make n with k integers.k integers will have to be choosen from k ranges.Every range has a minimum value and a maximum value.In how many ways we can make n according to the conditions.For example,k=4,n=10 and the ranges are : 1 1 2 2 3 3 4 4 we can make n in only one way.Another...

How to solve ii (b) ? Thanks in advance.

Let L be the level number of a bipartite graph G, and so L1 be the first level of n1 vertices, L2 be the second level of n2 vertices, ... Lk be the kth level of nk vertices. Then a bipartite graph G12 is created by a combination of L1 and L2, G23 is of L2 and L3,...,Gij is of Li and Lj. The...