Combinations Definition and 401 Threads

Doing some "how many combinations" calculation Homework Statement We're given the number 123215. How many different numbers can we get by changing the order of the digits? This is a six-digit number, so there are six positions for each digit. This is an unsorted selection with...

Homework Statement Let V = {f: \mathbb {R}\rightarrow\mathbb {R}} be the vector space of functions. Are f1 = ex, f2 = e-x (both \in V) linearly independent? Homework Equations 0 = aex + be-x Does a = b = 0? The Attempt at a Solution My first try, I put a = e-x and b = -ex. He...

Homework Statement 7 distinct flags are hoisted in a post. Find the number of ways of arranging them if 2 of the flags must be separated. (The answer is 3600) Homework Equations Permutation: n! Circular Permutation: (n-1)! The Attempt at a Solution 1: Flag 1, 2: Flag 2: The...

Homework Statement a series combinations is 11.6k ohms resistor and an unknown capacitor is connected to the a 180 V battery. One second after the circuit is completed, the voltage across the capacitor is 16.8v. determine the capacitance of the capacitor? Homework Equations V=18 C...

Homework Statement A family of nine has two vehicles, each of which can hold a maximum of five people. Homework Equations How many different ways are there of allocating people to the cars? If three of the memebers of the family only have a drivers licence, how many different ways...

Homework Statement If (u,v,w) is a family of linearly dependent vectors in vector space V and vector x is in the span of (u,v,w), then x=αu+βv+γw has infinitely-many choices for α,β, and γ. Homework Equations If (u,v,w) is linearly dependent, then there exists an α, β, and γ, not all equal...

Homework Statement Data set in X with mean xbar = 100 and standard deviation Sx = 10 Find ybar and Sy for 2(Yi-5)/10 + 7 Homework Equations The Attempt at a Solution All the problems I have seen are in the form yi = axi + b in which case the mean ybar = a(xbar) + b and...

Homework Statement Hello! Okay, using the letters AAABBBCCDE, draw three letters. What is the probability of getting exactly two letters the same? Homework Equations AND The Attempt at a Solution I worked my way through the possible combination (e.g. AAB, AAC, AAD, etc.) Then used...

What's the difference between these two: 1) The number of permutations of n distinct objects taken r at a time is \frac{n!}{(n-r)!} and 2) The number of combinations of n distinct objects taken r at a time is \frac{n!}{r!(n-r)!} ?

Homework Statement Not really a problem, just my understanding. What is the difference between them? I know the formulae are different. They seem to be the same thing, that is, n objects taken r at a time. Any help in clarifying this would be appreciated.

I am attempting to determine two probabilities in a scenario in which a classroom of 28 students with assigned seating is scrambled randomly and blindly reseated by the teacher. What is the probability that exactly one student is reseated in his or her original seat, and what is the probability...

The statement is that the image formed by the 1st lens acts as the object for the 2nd lens. For 2 thin lenses aligned along a common axis, would this statement be true for when the image formed by the 1st lens is real and past the 2nd lens (while ignoring the effect of the 2nd lens in this...

1. In Poker: A) A flush is 5 cards of the same suit not in any order. How many flushes are possible? B) A full house is 3 of a kind plus a pair. How many full houses are possible? 2. n C r (That's all I can think of right now) 3. For A) (13 C 5) / (52 C 5) = 33 / 66640...

Here's something I know there must be a way to easily figure out... but not by me! THE QUESTION... if I have x number of categories to choose from, how many combinations can I get? for example I think that if I had 4 categories there are 15 possible combinations categories A, B, C, D...

I have a question on complex analysis. Given a differential equation, \dfrac{d^2 \psi}{dx^2} + k ^2 \psi = 0 we know that the general solution (before imposing any boundary conditions) is, \psi (x) = A cos(kx)+B sin(kx). Now here's something I don't quite understand. The solution...

Homework Statement How many contestants have on one chess tournament, if every person have played only one game with all of the other contestants separately, and there are 210 games played. This problem should not be solved by variations, permutations or combinations. This problem should...

Homework Statement http://img234.imageshack.us/img234/8519/combgf7.png [/URL] Homework Equations {t}_k_+_1=_n{C}_kx^n^-^ky^k The Attempt at a Solution The picture I have shown contains the problem and the teacher's solution. However, I was wondering how the k value is 3. And no, I...

Homework Statement There are three girls and six boys on the school softball team. The team consists of a pitcher, a catcher, four infielders, and three outfielders. How many ways can the nine different positions be filled if the pitcher must be a girl and the catcher must be a boy...

Red light mixed with green light produces yellow light. Yet, a red photon and a green photon don't combine to make a yellow photon (or two of them). Can someone explain this?

Can someone please help with the method of how to solve this problem... Question: Three balls are thrown at random into 5 bowls so that each ball has the same chance of going into any bowl independently of wherever the other 2 balls fall. Determine the probability distribution of the...

Homework Statement The letters of the word POSSESSES are written on 9 cards, one on each card. The cards are shuffled and four of them are selected and arranged in a straight line. Homework Equations (a) how many possible selections are there of 4 letters? (b"how many arrangements are...

Homework Statement From 10 tickets of luck, only 3 are winning. If we buy 6 tickets, how many possibilities we have at least to have 1 winning ticket in our hand? Homework Equations C_n^k=\frac{n!}{k!(n-k)!} The Attempt at a Solution 6 tickets from 10, we can choose on C_1_0^6. There are 4...

I have two Lie algebras with structure constants f^{a}_{bc} and g^{a}_{bc}, the number of generators being the same (as will become clear). Due to a particular symmetry/construct, I have that the system needs to be valid under g \to af + bg (and a similar transform for g), which leads...

:cry: I can't solve it, please helpppp! problem :- there are 8 points in a plane (non collinear) find the maximum number of triangles formed out of these points such that no 2 triangles have more than one common vertex.

I have a set {1,2,3,4,5} and I need all possible combinations with three elements. Example {1,2,3}, {1,2,4}, {1,2,5} etc. Can somebody help me with a 'C' program that does this. I want to store {1,2,3} etc. in an array of size three and print out every time a new combination is formed...

Homework Statement Q #1 - A math teacher wants to give each student a 3 digit number using only the numbers 2, 3 and 6. Numbers can be repeated. How many possible combinations are there? Q #2 - (simplified) How many possible four digit combinations are there for the numbers 1, 2, 3 and 4...

Homework Statement A group of 12 friends goes to a cinema complex that is showing 6 different movies. If the group splits up into subgroups based on movie preferences, how many subgroup combinations are possible?Homework Equations nCr nPr (we can use calculators) The Attempt at a Solution...

In a varient of Poker each player is dealt a hand of 6 cards from a standard pack How many hands are there of each of the following types? Three pairs: Two cards of the same value. another 2 of a differnt value, and a 3rd paid of a third value. i.e Q(clubs) Q(diamonds) 6(hearts) 6(diamonds)...

This is an experiment Ill have to write up later, unfortunately I was out for 2 weeks of lectures due to illness. This is the experiment; Find the values of capacitance C and resistance R in a series combination, given he following apparatus; 1. the unknown RC combination (both in the same...

A 120-V circuit has a circuit breaker rated to trip (to create an open circuit) at 15 A. How many 300-ohm resistors could be connected in parallel without tripping the breaker? Given that, V= 120V, I = 15A, R= 300 ohm. Let the total resistance without tripping the breaker =...

I developed a php page that allows you to paste in text, and gives all the words listed alphabetically, and their counts in the text, tab delimited. http://www.cnetworksllc.com/word_lister for instance, if I type "the quick red fox jumps over the lazy brown dog" I get: brown 1 dog...

[SOLVED] simple combinations problem Homework Statement what is 12. combination of combinations with 3 elements of 1,2,3,4,5,6,7 ? Homework Equations The Attempt at a Solution i tried step by step 123 - 124 - 125 - 126 - 127 - 134 - 135 - 136 - ... - and finaly i arrived at...

hi there, my book didn't have an example like this so I am not sure what to do to solve it. Please explain how to do it, thanks. Express the following as linear combinations of p1 = 2 + x + 4x^2, p2 = 1 - x + 3x^2, and p3 = 3 + 2x + 5x^2 a.) -9 - 7x - 15x^2

need help on this? well guys i was doing some problems with series and i cam up with this problem, i think it belongs to combinatorics but i'll post it here. How is defined the permutations, combinations and variatons of negative numbers. For example if you were required to find the...

Springfield Football Club plan to field a team of 3 forwards, 4 mid-fielders and 3 defenders and a goalkeeper. Assuming they have 8 forwards, 6 mid-fielders, 5 defenders and 2 goal- keepers on their books how many teams can they make? i tried doing: (8C3) x (6C4) x (5C3) x (2C1) but...

Please tell me if there are motivated physical reasons to consider that combinations of dimensionless physical quantities that appear at the exponent of e in distribution functions have the same magnitude in all inertial reference frames in relative motion, Thanks in advance

Homework Statement Suppose that f(x) and g(x) are two eigenfunctions of an operator Q^{\wedge}, with the same eigenvalue q. Show that any linear combination of f and g is itself an eigenfunction of Q^{\wedge}, with eigenvalue q. Homework Equations I know that Q^{\wedge}f(x) = qf(x) shows...

Just to clarify these concepts: if a homogeneous system of linear equations with four variables z1, z2, z3, and z4 yields a matrix in reduced row echelon form that defines (as an arbitrary example) the linear equations z1 = z3 + 0.5z4 = t + 0.5s z2 = 2z3 - z4 = 2t - s z3 = t z4 = s...

Homework Statement i think i might have it right but i want a 2nd opinion (mainly part c) 31 flavors of icecream. we are picking 12 cones(1 scoop). a) cannot have same flavor twice b) can have any flavor up to 12 times c) can have any flavor up to 11 times but not 12 The Attempt...

Rubik's cube permutations I suck with really big numbers, so that's where you guys come in :) I basically want to know the number of permutations a 1000x1000x1000 Rubik's cube has, as well as a 5x5x5x5x5 Rubik's cube. Yes, a 5-dimensional one. I've been reading these a formula's, and...

Combinations! How many... Homework Statement How many letter combinations with 9 letters are you able to make with following letters : M-A-T-E-M-A-T-I-K? Homework Equations Well its pretty obvious you need to use Combinations. Please explain how you solve this problem, don't write...

Homework Statement Find the number of solutions to the equation x + y + z + t = 16, where x, y, z, and t are: i) odd integers ii) even integers Homework Equations N/A The Attempt at a Solution I know the total number of solutions is 19 choose 3. So I'm thinking I can obtain the...

Can someone explain to me how to do this problem... I am really lost... how many ways can you buy a dozen donuts from an unlimited supply of 5 types of donuts?

A subgroup must be formed, with 4 people being chosen from 3 larger groups. Group A contains 6 people Group B contains 4 people Group C contains 3 people The subgroup of 4 must contain atleast 1 person from each group (A,B,C). How many possible groups are there? Well there are 6...

Hey all, im taking geometry and discrete mathematics at my school. Its a 12 U course. And I am not doing as well as i would like in it. I am at about a 75, annd i want that to be around 85. So I am looking to you guys for some help. If you guys wouldn't mind awnsering a few questions i have...

Question regarding two lenses in combination - the first is a diverging lens with f = -31.5 cm, and the second is a converging lens, 14 cm away, with f = 20.0 cm. The exact question is 'Where will an object at infinity be focused?' (coming in through the diverging lens), and I kind of understand...

Hi, I have some queries that I'm hoping you can help me with. Actually these are probably fairly straight forward for this forum but it's been a long time since I've done any formal math so some help would be appreciated. First query: suppose I have 4 objects: A, B, C and D. I want to know...

Homework Statement Find the equivalent capacitance between points a and b for the group of capcitors connected as shown below. http://img250.imageshack.us/img250/7816/40ha4.th.png Homework Equations Series/Parallel combinations. The Attempt at a Solution I don't get how the...

Hi, just joined this forum, I am an EE undergrad and trying to find a solution to the following assignment, hope somebody here could help or point me in the right direction. Given some resistor values (1.8ohm, 20ohm, 300ohm, 24kohm, 56kohm) I must construct series and parallel combinations...

Surely there's an easier way to do this question than the method given? Q: Two couples and one single person are seated at random in a row of five chairs. What is the probability that neither of the couples sits together in adjacent chairs? A: Yes. Let's call the first couple C and c, the...