Combinations Definition and 415 Threads

A witness to a hit-and-run accident tells the police that the license plate of the car in the accident, which contains three letters followed by three digits, starts with the latters AS and contains both the digits 1 and 2. How many different license plates fit the description?

Homework Statement I am having trouble determining the error for a set of linear equations that represent a simple circuit with two voltage sources. I have found two possible uncertainties by solving using substitution, detailed below. The circuit is shown below...

Homework Statement Find the sum of all numbers greater than 10,000 formed by using the digits 0,2,4,6,8, no digit being repeated in any number. The Attempt at a Solution I can't think of any method of approach. A hint will help.

Homework Statement There are n points in a plane which are joined in all possible ways by indefinite straight lines, and no two of these joining lines are parallel and no three of them meet in a point. Find the number of points of intersection, exclusive of the n given points. The...

Homework Statement This is something I want to know regarding a game series I am a big fan of. If we are given a certain amount of points that can be distributed among a certain number of different skills, with the added restriction that each skill has a maximum number of points that can be...

Homework Statement How many 4-letter codes can be formed using the letters A, B, C, D, E, and F? No letter can be used more than once. Homework Equations N/A? The Attempt at a Solution I really didnt know where to begin . . .

Will there always be two different combinations that produce b=(0,1) of three vectors: u, v, and w? I'm pretty certain that the answer is no, but am I right in saying that with three vectors, assuming they are not all parallel, will always have at least one combination that produces (0,1)

The linear combinations of v=(a,b) and w=(c,d) fill the plane unless _____. Find four vectors u, v, w, z with four components each so that their combinations cu+dv+ew+fz produce all vectors (b1, b2, b3, b4) in four dimensional space. I think that the first part of the answer, that fills the...

How many permutations (when objects are not all distinct) of size k can be created from a set of size N composed of n1, n2,n3,...,nr parts? When k = N this is easy and is equal to N!/(n1!n2!...nr!) The following question would be then how many combinations (when objects are not all distinct)...

In how many ways 7 persons can be selected from 5 indian, 4 british and 2 chinise, if atleast 2 are to be selected from each country.

Hey every body... I have been trying to figure this out for quite a while now... and i feel like i am making progress, but it just doesn't seem to be working. Imagine you have a string of numbers with a length of X N of those numbers must be 1 and X-N of those numbers must be zero. how...

I would like do estimate the total number of different pictures I can represent by choosing a specific resolution and color depth, the number I'm getting seems somewhat low, so I'm wondering what am I doing wrong ? Let the picture size be 45x45pixels with a color depth of 8 bits (2^8 = 256...

Hello, I am currently generating a campaign of experiments in where I have four factors (conditions like temp, pressure, etc.) at different levels. I am looking to find out the total number of factor combinations, or essentially the total number of condition combinations, that I will have at...

Hey guys (and gals), I've been wondering whether there's an intuitive way to understanding combinations with repetition, so that you would just use the basic rules of the sum and product instead of going with the handy formula that pertains to said combinations. I had an example where in...

Homework Statement a) 8 new teachers are to be divided among 4 schools, and each teacher can teach at maximum 3 schools. There is a staff limit such that 3 of the schools only allow 4 new teachers. How many divisions are possible? The Attempt at a Solution Without staff limit a) So if...

Hi, I have a question regarding the CP operator on pion systems. 1) CP \mid \pi^0 \rangle 2) CP \mid \pi^+ \pi^- \rangle 3) CP \mid \pi^0 \pi^0 \rangle I'd like to solve this in the above ket notation and apply the operators as is on the different parts of the represented wave function...

Suppose I have a set containing 40 elements, 20 of these elements are identical, and the 20 other are identical. Suppose an ordering is some list of all elements of this set, how many different orderings are there? These types of questions were never my forte and I have no idea how to go...

Firstly, sorry if this is in the wrong place. I'm new here. Seems to be an awesome site! :) Homework Statement Well, I've got to learn all these formulae (regarding the periodic table) and was wandering if there's any specific way to be able to understand when something is and Oxide or...

Homework Statement If k people are seated in a random manner in a row containing n seats (n>k), what is the probability that the people will occupy k adjacent seats in the row? I realize that there are n choose k sets of k seats to be occupied, and that there are n-k+1 sets of k adjacent...

Q in permutations and Combinations Out of a standerd 52 - card deck . how many 6-card will hearts and 2 clube ? my answer : 13 C 4 X 13 C 2 = 715 X 78 = 55.770 this is my answer please help me ...

Hi I want simple explanation of the Permutations and combinations and which one has condition and I want simple example to undersand it I want your help

Hi all, I am working on a programming project and want to know how many possible combinations can exist in a particular situation, but I have no idea how to work it out. It isn't homework, I just want to know because I am sure it is a VERY large number and want to make a point. There are 2...

This is a problem I created for myself, and I've been thinking about for a while and would like some other opinions on the matter. I'm using simple numbers just for example. The problem: Suppose you are hungry, and you need to eat at least 10 calories worth of food to get full, and you'd...

Homework Statement There are a total of 30 members of Parliament in a new country called JanesWorld. Among these deputies, there are 10 from the “Conservative Janes” , 8 from the “Progressive Janes” and 12 independents . How many ways can Queen Jane form a parliamentary committee of 11...

Homework Statement 1) What is the coefficient of x^43 in the expansion of [(2/x^2) − x3)^16? (2) What is the coefficient of x^14y^12 in the expansion of (3x − 2y)^26? Homework Equations Binomial Expansion The Attempt at a Solution For (1), I started out like this: (16...

Hello; My physics teacher asked me to name the combinations of quarks that could make up a proton and a neutron; uud = proton udd = neutron But is that all? Does it have to be 2 up quarks and 1 down quark to make the proton? Why not 2 charm quarks and 1 strange quark, for example? Or 2...

Homework Statement Each of 12 refrigerators of a certain type has been returned to a distributor because of the presence of a high pitched oscillating noise. Suppose that 5 of these 12 have defective compressors and the other 7 have less serious problems. If they are examined in random order...

Homework Statement Each of 12 refrigerators of a certain type has been returned to a distributo because of the presence of a high pitched oscillating noise. Suppose that 5 of these 12 have defective compressors and the other 7 have less serious problems. If they are examined in random order...

The questions is pretty short... The source was a chat session and hence the simple sentence. I am stuck with this and thought that Homework Help doesn't attend out of the way questions and so I'm asking them here.

Hi there I was wondering if there is a simple way to solve for the roots of a complicated summation of trig functions that can't be combined with any simple identities. I have an equation of the form: 0 = sin(8x-arctan(4/3))+3.2sin(16x+pi/2) where the two sines have different amplitudes...

Two chemicals, A and B, are combined, forming chemical C. The rate of the reaction is jointly proportional to the amounts of A and B not yet converted to C. Initially, there are 50 grams of A and 80 grams of B, and, during the reaction, for each two grams of A used up in the conversion, there...

for a given combination of metals phase transformations occurs at a variable temperature which is in between the phase change temperatures of constituting metals except at eutectic combination. why at this combination phase transformation is taking place at a constant temperature? what is the...

if you are given an amount of cents, and a set of coin denominations...how can we tell if its impossible to amount to exactly the given amount of cents? for example say we want to gather 8 units of value but only have coins with denomination 3 and 7, thus its not possible to make a combination...

Hello. I've been struggling with this problem for some time, and honestly I do not know how to solve it. Homework Statement Two positive lenses are to be used as a laser beam expander. An axial 1.0 mm diameter beam enters the short focal length positive lens, which is followed by a...

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...

Homework Statement Write the vector (1,2,3) as a linear combination of the vectors (1,0,1), (1,0,-1), and (0,1,1). The attempt at a solution (1,2,3) = C1(1,0,1) + C2(1,0,-1) + C3(0,1,1) The matrix for this is: 1...1...0...1 0...0...1...2 1...-1...1...3 I reduced it to the...

Homework Statement A production facility employs 20 workers on the day shift, 15 workers on the swing shift, and 10 workers on the graveyard shift. A quality control consultant is to select 6 of these workers for in-depth interviews. Suppose the selection is made in such a way that any...

Homework Statement I was wondering for what situations one uses the formula: (nCr x nCr)/ nCr ? Thanks Homework Equations nCr

Review problem. I have the answers. Don't know how to get them. Answers in brackets. Homework Statement Shortly after being put into service, some buses manufactured by a certain company have developed cracks on the underside of the main frame. Suppose a paricular city has 25 of these...

Can someone please explain to me how to do combinations?

Hi all. I recently am thinking of developing a compression software with extreme speed and compression. The simple principle behind the working of this software is that the software is converting the program into binary code. Then, five sets of 0s and 1s are converted into alphanumeric...

Homework Statement a license plate has 3mos then 3letters then 3nos(numbers) if there are no constraints how many license plates are possible Homework Equations 9x9x9x9x9x9x9(..maybe) The Attempt at a Solution The same as the one above, I am very confused.

Hey there, I'm currently a first year physics student at the University of Western Ontario (UWO), and intent to register is approaching (March, I panic easily) and I really need to think about what modules I want to take. The way it works here is you have 20 credits to get for a 4 year...

Homework Statement There are 15 boys and 19 girls in a room. a) Find the number of different groups that contain exactly four girls and five boys. b) How many groups of 14 have an equal number of boys and girls? c) How many groups of 5 have more boys than girls? Homework Equations...

Here is a list of sums rolled by 4 six-sided dice. The number of combinations for each sum is given below each sum. ...sums: 4 5 6 7 8 9 10 11 12 13 14 combinations: 1 4 10 20 35 56 80 104 125 140 146 ...sums: 15...

Lets say you have a bunch of projects to do, says project 1,2,3,4,5. You don't have to do them all, in fact you don't have to do any of them...and the order you did them in has no effect on how they come out. how many ways can this be done? examples, 12, 1234, 234 or no projects at all edit...

hello.i need some help.i need to know how many possible combinations of 5(abcde etc.) are there in 12( abcdefghijkl)eg.their are 12 games of hockey that can end in a tie(shootout).each game is designated as a,b,c,d,e,f,g,h,i,j,k,l. 5 of the games will be tied.i need to know how many possible...

Homework Statement To gain access to his account, a customer using an automatic teller machine (ATM) must enter a four digit code. If repetition of the same four digit is not allowed (for example, 1111), how many possible combinations are there? The Attempt at a Solution I figured two...

Homework Statement A candidate sitting this paper is told to answer 5 of the 7 questions in section A, and 3 questions from the 5 options in section B, where not more than 2 questions from the same option can be chosen. Assuming that he answers 8 questions altogether, find how many different...

Homework Statement Question B only Homework Equations The Attempt at a Solution 1) Why we use f=15.0cm? Shouldn't it be f=infinity considering plane mirror have an infinity focal length? 2) Normally I do combination(lens, mirrors), firstly I will consider the front...