Combinations Definition and 415 Threads

there are 4 circles and 4 straight lines...find the maximum number of intersecting points possible in the intersection of all these given figures...i can't get how to solve it...

Hi. I need a little help. I'm trying to work out how many combinations of characters there are for a string that is between 1 and 8 characters long and uses a-z (non caps) and 0-9. There are 36 useable characters and the string could be anything from simply 'a' to '99999999'. I was able to...

Homework Statement Suppose 5 cards are dealt at random from a well shuffled, 52 card deck. The hand can be thought of as a random sample size 5 from 52, with no replacement. What is: (a) P (4 aces) (b) P (3 aces and 2 kings) (c) P (4 of a kind) Homework Equations I know the...

Hi If i have 3 4x1 matrices and i want to check if i can express a 4th matrix as the linear combination of the first 3. my 3 vectors: 1 7 -2 4 10 1 2 -4 5 -3 -1 -4 can this vector be expressed a linear combination of the first...

Homework Statement Find Rth, at the terminals shown on the diagram Homework Equations Series resistance = R1 + R2 + R3 +... Parallel Resistance = 1/((1/R1)+(1/R2)...)) The Attempt at a Solution When attempting problems like this, I was told by teachers and the textbook to...

Algorithm for finding best (or combinations of) "non-overlapping" matrix elements. I'm looking for the best general way to find the "best" combination for a list of non-overlapping matrix elements. For example, given the matrix AE BE CE DE AF BF CF DF AG BG CG DG AH BH CH DH...

Hi, My question is related to a math puzzle. The puzzle asks to swap any two digits from the numerator with any two digits in the denominator of the fraction 1630 / 4542 to get the ratio 1 / 3. Two possible answers are 1534 / 4602 and 1354/ 4062. What I am struggling with is the number...

Hey everyone, I have a question regarding combinations and poker! Could someone explain to me why the number of distinct ways to receive a full house from a five card draw is: 13 nCr 1 * 4 nCr 3 * 12 nCr 1 * 4 nCr 2 and not, 13 nCr 2 * 4 nCr 3 * 4 nCr 2 I usually make small...

Homework Statement There are 10 cricket matches are on to start and each match can result three types of wins i.e. either first team win or draw or second team win. How many combinations can possible to make all the cricket matches should be right, if a user select only one option per...

Homework Statement I have questions along the line of Use the Euclidean Algorithm to find d= gcd(a,b) and x, y \in Z with d= ax +by Homework Equations The Attempt at a Solution Ok so I use the euclidean algorithm as I know it on say gcd (83,36), by minusing of the the...

You roll thirty dice. How many different possible combinations can be rolled? Order does not matter I think it's 6^30 choose 30, so: \frac{(6^{30})!}{(6^{30}-30)!(30!)} Also, perhaps the more important part of my question - any idea how to approximate this? The numbers involved are very...

Forgive me for not writing in latex, but I searched this site for 10 minutes looking for a latex reference and could not find anything on matrices. Also, excuse for the excessive amount of info. Homework Statement Determine whether this list of 3 polynomials in P1: p1 = 1+3x p2 = 1+2x...

Homework Statement Let g: ℝ→ℝ satisfy the relation g (x+y) = g(x)g(y) for all x, y in ℝ. if g is continuous at x =0 then g is continuous at every point of ℝ. Homework Equations The Attempt at a Solution Let W be an ε-neighborhood of g(0). Since g is continuous at 0, there is...

Homework Statement Prove that for any positive integer n, k, $$\binom{n}{2k+1}=\sum_{i=1}^n{\binom{i-1}{k}\binom{n-i}{k}}$$ Homework Equations $$\binom{n}{k}=\frac{n!}{(n-k)!k!}$$ The Attempt at a Solution I'm looking for a starting point. I've been given a hint that says, But I don't know...

Need a little help here, if anyone can offer any advice. The problem I have is this. I have a dictionary that contains keys, and their possible values. I need to generate every possible combination of key values where each key can take on one of the possible values. For example, the...

Hi, Can anyone give me an idea of how to be able to browse through a set of combinations? Lets say that I have 3 objects that can hold 3 different values and I want to browse through these. How do I know which is the next combination? I will always know how many values every object can...

Four married couples attend a wedding dinner. One of the couples brought along two children. Find the number of ways in which these ten people can be seated round a table if each couple must sit together. I need to know the logic and thinking process behind how the answer is derived. What I...

Homework Statement The question states: "find all scalars c, if any exist such that given statement is true." It also suggests trying to do without pencil and paper. a) vector [c2, c3, c4] is parallel to [1,-2,4] with same direction. b) vector [13, -15] is a linear combination of vectors...

I'm trying to work out the proof of combinations with replacement, but I can't quite understand the result of it. (n+k-1)ℂ(k) is the result, could somebody please explain this to me?

I'm trying to figure out the formula I need...ok, say that r=5, so there are 5 items {A,B,C,D,E} And we want to chose 5 of those Order doesn't matter, repitions allowedso for example {A,A,A,B,B} is a feasible solution {A,B,C,D,E} is feasible so on But the formula (n+r-1)!/r!(n-1)! doesn't...

small FORTRAN code for combinations. BUG! PROGRAM test implicit double precision(a-h,o-z) INTEGER :: r=2,n=4,k=1 INTEGER,allocatable :: comb(:) !array to hold a set of combinations allocate(comb(r)) comb(1)=1 CALL iterate(1,n-r+1,1) CONTAINS...

Homework Statement So 5 numbers are drawn from pile of 10 balls. After the draw, the ball is put back in the pile. So you always have 10 choices for the ball.After drawing 5 balls, another one is drawn for the sixth number. What is the chance of getting the winning number-combination 848235...

Homework Statement Students are playing a lottery game. In this game, three numbers are drawn from a set of six. If the three numbers on a student's ticket match those drawn, the student wins the full prize. If just one or two numbers match, the student wins a consolation prize. The...

Hello, I have a small problem/puzzle to solve which goes as follows: (I have already calculated it, however I am not sure I followed the right reasoning as mathematics is not my strong point and after building a Java app to brute force it, it crashed on out-of-memory error)...

Hi. If you have a 3x3 grid of dots, how many different paths can you draw if you have to go through each dot? There can be crossing lines, but none overlaping. e.g.: 158 924 637 Sorry for my formulation. I didn't copy this from somewhere, it's a practical problem.

I have been trying to figure out a formula for the sum of combinations. For example: \sumnk=0(\frac{n}{k}) = 2n But what if you want to sum from any arbitrary k, like 4? I've tried looking at Pascal's triangle for nice values of n and k, but haven't been able to see a pattern. I would...

Hi, I am not sure which formula will allow me to get the following results. If I have to pick two letters from A, B, C, D, then there are 6 possible combinations: AB AC AD BC BD CD. Now assume that letter D has turned into another A, i.e. A2. Now my combinations have changed...

The dean of an Engineering School invites all 9 department chairpersons and their spouses to his house for a Winter Solstice party. If each department chair may attend without a spouse, but the spouse may not attend without the department chair, how many different sets of attendees are...

Hi, Before ask my question, let me explain how this game works. It exist a board with 9 positions and 9 pieces. Each position of the board is for a piece. A piece is composed by four symbols on each side. Each piece must match their neighbors, and each one can rotate. The goal of this game...

Homework Statement From a group of 3 freshman, 4 sophomores, 4 juniors, and 3 seniors, a committee of size 4 is randomly selected. Find the probability that the committee will consist of: a) 1 from each class b) 2 sophomores and 2 juniors c) only sophomores and juniors Homework...

Hello, I am a graphic designer working on a menu for a friend of mine and math was never my strong suit. Also, add the fact that I've been out of school for some time and don't do math regularly. Anyway, I have a pretty simple question that I could use some help with if someone doesn't mind...

Could Someone tell me how to calculate any 8 digits, to two 4 digit combinations, with non of them repeating/conflicting except for the two 5's, such as 4589, 8945? the 8 digits I'm specifically interested in is 23455689? please don't give just a formula, unless you can explain how to input...

Hi all, I'm new to the forum, this is my problem: given a positive integer n, i want to find how many combinations of integers smaller than n but larger than 0 sum to n. E.g. n=3: {3},{2,1},{1,1,1} n=4: {4},{3,1},{2,2},{2,1,1},{1,1,1} it might just be that I'm tired, but I've been...

I want to see if the matrix w = (1,0;0,1) is a linear combination of the matrices v1 = (1,2;-2,1) and v2 = (3,2;-1,1) where ; denotes a new line in the matrix. I know for example if w and v were 1xn matrices i.e vectors such as w = [1,1,1] v1= [2,-1,3] v2=[1,1,2] then i setup a matrix with...

Hi there. I have a question about combinations at the Math 12 Principles level. Homework Statement From a group of 5 student representatives, 3 will be chosen to work on the dance committee. Also, each committee must have a chairperson. How many committees are possible? The Attempt at a...

How can one find the number of combinations of a list such as {2,2,2,2,2,2,2,3,3,3,3,5,7} (7 2s, 4 3s, 1 5, 1 7). I am pretty sure that the answer is 160 (the number of proper divisors of 9!). How can I figure it out using combinations/permutations or some other method?

Homework Statement In how many ways can 12 balls be arranged into 4 different rows with each row having at least one ball if there are 6 identical red balls and 6 identical white balls? Homework Equations number of combinations of N objects into r groups is \frac{(N+r-1)!}{N!(r-1)!}...

I'm sorry, I didn't really know where to post this question, so I posted it here, because it is the closest to Data Management, I think. There are 19 students in the classroom. The students are seated in a circle. Each student shakes the hand of the person sitting to the left and the right of...

Homework Statement Find the number of different arrangements of the name "BENNETT TAN" with all the T's separated and all the N's separated. Homework Equations The Attempt at a Solution I have no idea how to start this question. If anyone is so kind to help me. Thank you. I...

I am facing an issue in my research where I need to enumerate all combinations of an underlying set. BUT the set has some special features. Here is an example: Given a set {A,B,C,D,E, F} where each item in the set consists of two values. Something like: A = (1,2) B = (3,4) C = (5,6)...

I have a rather difficult math problem. In my circuits class the professor prefers to express the cosine function using Euler's formula as (ejwt+ejwt)/2. Last semester for the final, one of the problem's solutions (that he gave us) used partial fraction decomposition to solve the Laplace...

Hi If i have many 3 digit number which are all different and can not be zero,and have to make as many 2 digit numbers from each one of them. They all give me 6 different 2 digit numbers. What pattern will this follow in general? And what will the sums of the 2 digit numbers have in common...

Homework Statement We are given the following subspaces U := {x E R3: x1 + 2*x2 - x3 = 0} and V := {x E R3: x1 - 2*x2 - 2*x3 = 0} And we need to find a basis for (i) U (ii) V (iii) U n V (not an "n" but a symbol that looks like an upside-down U) (iv) span(U u V) (not a "u" but a symbol that...

The question is as follows: Suppose a lot of 50 electrical components contains five components that are defective. The lot is randomly divided among five customers, with each customer receiving 10 components. Calculate the probabilities of the following events: a. Each customer receives one...

It is easily shown that two eigenfunctions with the same eigenvalues can be combined in a linear combination so that the linear combination is itself an eigenfunction. But what if the two eigenvalues are not the same? Can you still find a linear combination of the two functions that is an...

I need to confirm something about combinations: 1. I need to find the combinations of 5 out of 35. <=> 35C5 = 324.632 combinations. 2. Now I want to try to "fit" these 324.632 combinations of five numbers into sets of 6 numbers. To do that, I first find how many combinations of five numbers...

My mom has a Texas Instruments TI-36 Solar calculator. A few days ago I found that there are functions for calculating combinations and permutations. The trouble is I can't seem to figure out how to use them.

Homework Statement A soccer coach organizing a field trip finds that 50 students have signed up. However, the bus has only 47 seats, so a few students will have to travel by car. The coach and one other coach must go on the bus. Explain two different methods for using combinations to find...

Homework Statement Determine how many odd 4-digit numbers with all of the digits different can be made from the digits 0 to 7 if there must be a 4 in the number. Homework Equations The Attempt at a Solution First way (the "4" in the first spot) 1X6X5X4=120 2nd way ("4" in second...

Hi, I am trying to understand some of the basics of differential geometry in respect to general relativity. However, I not sure that I understand what seems to be a fairly fundamental bit of maths connected with the generic metric given in [1]. For simplicity, the notation has been reduced to...