Counting Definition and 392 Threads

Homework Statement Billy has 1 penny, 1 nickel, 1 dime and 1 quarter. How many different ways can he put his coins in the following board by placing one coin in each cell? Juan walks to school everyday. His walking speed is 1/15 mile per minute, and it takes him 30 minutes to get to...

Hi everyone. I thought I understood this problem, but now I'm unsure. Everything is worked out step by step with the answers, but when I try to duplicate it, I get something different. Can anyone shed some light on it? Homework Statement Suppose there is a steady current of 0.50 A in a...

Homework Statement I am wondering is there a way to count the number of bits to the left or right of a given 1 in a 32-bit integer? For example, if I give the function the number 32 = 0b100000, there are 5 bits to the right of the 1 and hence, 26 bits to the left of the 1. The catch...

Hi all, I am wondering is there a way to count the number of bits to the left or right of a given 1 in a 32-bit integer? For example, if I give the function the number 32 = 0b100000, there are 5 bits to the right of the 1 and hence, 26 bits to the left of the 1. The catch is, is there a way...

How many divisors does 55,125 have? For example, 55,125 = (3)^2 . (5)^3 . (7)^2

Homework Statement let f(x)=x^3+x^5. Evaluate int((f(x)^-1)^2, x = 0 .. 2) The Attempt at a Solution i have a feeling that it has a relation with counting volume of a solid revolution.but i don't know how to answer it...

PI(N) = N /{A * LOG(N)^2 +B * LOG(N) + C}. Note: LOG(N) is the common log. This formula works for N up to 10^23. The accuracy depends on the number of digits after the decimal point in the coefficients A, B & C. I used a Lotus123 spreadsheet to calculate them. My calculated values are...

In a math contest, the question goes somehow like this: A lattice point is a point wherein the value of (x,y) is an integer. Determine the total number of lattice points in a circle which has a radius of 6 and the its center is at the origin. Any one knows the solution or shortcut for this?

I have trouble finding the following information on the coincidence counting in a Bell experiment: - Is there a fraction of single photons (not entangled) produced in the experiment and how are the final results corrected for this? - No-hits on both side can never be counted (nothing is...

A calculator has an eight -digit display and a decimal point that is located at the extreme right of the number displayed, at the extreme left or between any pair of digits. The calculator can also display a minus sign at the etreme left of the number. How many distinct numbers can the...

Homework Statement How can you get from this \frac {z(i-1) +i +1} {z(1-i) +i +1} to this = \frac { z-1 } {-z -i} ? The Attempt at a Solution SageMath does not simplify the result any further from the beginning. The equivalence is based on some high Math. I am not sure how you...

Let’s say i have n identical classical non interacting particles and N sites where i can put them in. BUT the total energy is given. The number of possible states is (N)^n/n!/(n/2)! Where N^n is the total possibilities to arrange the particles. We divide it by n! since they are identical...

Jackson: t-minus three semesters and counting! Okay, help me with this thought-experiment: I was wondering how well-prepared for graduate (Jackson) electromagnetism I would be if I had studied the entirety of Griffith's "Intro...Electrodynamics" one year beforehand. What subject-matter would I...

Theorem: Let {N(t): t≥0} be a Poisson process of rate λ. Suppose we are given that for a fixed t, N(t)=n. Let Ti be the time of the ith event, i=1,2,...n. Then the (conditional) density function of Tn given that N(t)=n is the exactly the same as the density function of X(1)=min{X1,X2,...,Xn}...

Let {N(t): t≥0} be a Poisson process of rate λ. We are given that for a fixed t, N(t)=n. Let Ti be the time of the ith event, i=1,2,...,n. Then the event {T1≤t1, T2≤t2,...,Tn≤tn, and N(t)=n} occurs if and only if exactly one event occurs in each of the intervals [0,t1], (t1,t2]...

Homework Statement Show that there is a one to one correspondence between even and odd subsets of the set {0, 1...n}. Homework Equations They want a combinatorial proof so basically a proof based on counting? Perhaps (n choose k) = (n choose n-k) The Attempt at a Solution I've...

Evan pulls one marble randomly from a bag containing 6 red marbles, 3 green marbles, and 1 yellow marble. What is P(red or yellow)

Homework Statement A committee of seven is to be chosen from 8 men and 9 women. a) how many possible committees are there? b) how many committees contain at least 6 woment? c) if bob and alice cannot be on the same committee because they cannot work together well, how many committees are...

Homework Statement how many 4 digit positive integers have at least one digit that is a 2 or a 3? Homework Equations - this is what I need - The Attempt at a Solution I cannot find the equation to this problem. Can someone give me a hand?

[FONT="Comic Sans MS"]could some1 help me in these 3 questions of C language Q1 Write a program to count the number to count the number of zero’s, one's, blank spaces and other characters using switch statement. Q2 Write a program to evaluate the series x-(x^3)/3!+)(x^5)/5!-(x^7)/7! ...

Three drugs: A, B and C 50 subjects reported relief from: 21 drug a 21 drug b 31 drug c 9 a&b 14 a&c 15 b&c 41 report relief from at least one drug Note that some of the subjects who reported results from A might have done so for B and C etc. a. How many got relief from...

Homework Statement Suppose you have an a x b rectangular array of distinct integers (think of it as a matrix if you would like). Now suppose we first move across the columns and take a permutation of the entries in each column. Informally, we can imagine the integers in the array as cards, and...

Is there a longest repeated sequence (congruency) in the prime counting function \pi (x) (that which gives the number of primes less than or equal to x)? Recall that \pi (x) , although infinite, may not be random, and itself starts out with an unrepeated sequence \pi (2)=1 and \pi (3)=2...

Homework Statement An organization of 100 members, 6 of whom are officers, plans to elect delegates to attend a convention. There are to be 2 delegates; one must be an officer and the other cannot be an officer. In addition, an alternate delegate, either an officer or not, will be elected and...

1. Homework Statement [/b] There are N 3-dimensional quantum harmonic oscillators, so the energy for each one is: E_i = \hbar \omega (\frac{1}{2} + n_x^i + n_y^i + n_z^i). What is the total number of states from energy E_0 to E, and what is the density of states for E? The Attempt at a...

my question is, let us suppose we can find an expansion for the prime number (either exact or approximate) \pi (x) = \sum _{n=0}^{\infty}a_n log(x) and we have the expression for the logarithmic integral Li (x) = \sum _{n=0}^{\infty}b_n log(x) where the numbers a(n) and b(n)...

how many 1 dimensional subspaces of Z_3^3 are there? Z_3^3 has 3^3 = 27 vectors 26 of which are non zero then we can say v and 2v have the same span and so there are in fact 13 1 dimensional subspaces. is this true?

Homework Statement Suppose that tosses of a biased coin in which it comes up heads with probability 1/4 are independant. The coin is tossed 40 times and the number of heads X is counted. The coin is tossed X more times. A) Determine the expected total number of heads generated by this...

I have heard many people use the term power counting before but I can't find any explanation of what it means. All I know is that it is related to renormalisation somehow. Could someone explain to me what power counting is? thanks

The problem statement Suppose you have n beads, each with a different color. You need to string these beads into a necklace. How many distinct necklaces can you make? (A necklace flipped over remains the same and does not count as a distinct necklace.) The attempt at a solution I...

The problem statement There are 26 letters in the English Alphabet, how many seven-letter palindromes can be made? The attempt at a solution There are 26 letters in the alphabet, so there are 26^7 possible strings of length 7 (order being important for palindromes, i don't think 26...

Wikipedia article Hilbert-Polya conjecture has a link to an article H=xp and the Riemann zeros by Berry & Keating. They mention that the number of energy levels below given E could be counted by computing the area enclosed by the contour H(x,p)=E in the phase space. What is that all about? Does...

Homework Statement Here's the problem. We define the triple primes as triples of natural numbers (n,n+2,n+4) for which all three entries are prime. How many triple primes are there? (Hint:mod 3.) (By way of contrast, it is not yet known whether the twin primes-that is, pairs (n,n+2) with both...

Homework Statement In the measure space {X,S,u} where u is the counting measure X=(1,2,3,..} S= all subsets of X fn(x)=\chi{1,2,,,..n}(x) where \chi is the characteristic (indicator) function. Does fn(x) converge a.pointwise b.almost uniformly c.in measure Homework Equations...

Homework Statement Given that the ASCII character system has 128 possible characters how many 5 character strings are there with at least one occurence of the '@' symbol. Homework Equations The Attempt at a Solution So clearly which symbol we're using doesn't matter, and I see...

Short version: What is the difference between the Lebesgue measure and the box counting dimension of a set? Long version: I was reading up on the definition of the Lebesgue measure, and the description of how to take the Lebesgue measure of a set (which I understood basically as "cover the...

I'm calculating the high-water marks for the following function: f(n) = #{n is a k-strong pseudoprime, 1 < k < n} where n is a composite integer. The naive Pari code: ff(n)=sum(k=2,n-1,isSPRP(n, k)) record=0;forstep(n=3, 1e6, 2, if(isprime(n), next); k = ff(n); if (k > record, record = k...

I'm trying to show that for two permutations f ang g in Sn, the number of disjoint cycles in fg is the same as the number of disjoint cycles in gf. I know that in general fg does not equal gf, but by working examples it seems like they always decompose into the same number of disjoint cycles...

HTML -- counting the number of responses from a text file Hello, I have an angelfire website and on one of my pages I ask a simple question. What is your shirt size? There are four options: Small, Medium, Large and Extra Large. The answer is then submitted to a text file. My problem is...

We have Canberra Multiport II with 5 ADCs and coupled to Ginie 2000 software using USB key, we are using only one ADC no #3 currently. Counting is carried out for preset number of counts under single ROI. The counting automatically stops mostly at around 2200 hrs or 0000 hrs or 1000 hrs. This...

Homework Statement Let p be a prime. (a) Determine the number of irreducible polynomials over Zp of the form x2 + ax + b. (b) Determine the number of irreducible quadratic polynomials over Zp. The attempt at a solution A nonzero, nonunit polynomial f(x) in Zp[x] is irreducible if it...

moe in wichita ks how many drops are in 1 inch of rain on a 1 inch dia tube? of course iam guessing that all rain drops are the same size, which most likely they are not. sounds the like this is going to have a lot averages in the answer.

Homework Statement a) if jack has 10 friends, in how many ways can he invite 5 of them to dinner. b) suppose 2 friends don't like each other, and if one is invited, the other can't come. c) what if 2 of the friends are married and if they invite that friend, the spouse must come. Homework...

A seven-digit phone number in the United States consists of a three-digit exchange followed by a four-digit number. How many exchanges are needed to serve a city of 80,000 people? Combination, Permutation, and arrangement with repetition equations are used in this section. Part 1 of...

How many sets of four consecutive integers are there such that the product of the four integers is less than 100,000? Set_1=1,2,3,4 Set_2=5,6,7,8 Set_3=9,10,11,12 Set_n=a\cdot b\cdot c\cdot d<100,000 Okay, I know I could continue with my Sets, but there has got to be a more logical approach...

Homework Statement I am having trouble with this problem. A network of city streets forms square bloacks as shown in the diagram below. http://img182.imageshack.us/my.php?image=librarypoolqs6.jpg Jeanine leaves the library and walks toward the pool at the same time as Miguel leaves the pools...

Hi All, I am trying to reconcile two approaches used in counting problems. The first approach uses combinations and the other uses probability. I understand the combinations approach, but not able to comprehend the probability approach. Consider the following example, A carton contains...

Hi last one here. Any hints on this is appreciated too :) Let G be a group of order 44. Show using Sylow's counting that G has a normal subgroup of order 11. Use the results to classify all groups of order 44.

Hey there guys. Let G be a group of order 12. Show by a Sylow counting argument that if G does not have a normal subgroup of order 3 then it must have a normal subgroup of order 4. Deduce that G has one of the following forms: (i) C_3 \rtimes C_4 (ii) C_3 \rtimes (C_2 \times C_2) (iii) C_4...

Homework Statement The question says: A chain of stereo stores is offering a special price on a complete set of components (reciever, compact disc player, speakers). A purchaser is offered a chocie of manufactuer for each component: Reciever: Kenwood, Onkyo, Pioneer, Sony, Yamaha Compact...