Combinations Definition and 401 Threads

Homework Statement There are 6 males and 4 females awaiting to see a teller at a bank. Only 4 people can be served at one time. 1) How many ways can four of the people be picked and served one at a time, if they must include two(2) men and two(2) women? 2) If indeed the four people...

hey , just wondering about gluons : red - anti red red - anti blue red - anti green blue - anti red blue - anti blue blue - anti green green - anti red green - anti blue green - anti green Our common sense tells us there's 9 , but in reality there's 8, how come ? I have already...

Hello everyone, Another example from the book I'm going over and I'm not exactly sure how they got their answer: The game of poker is played with an ordinary deck of cards. Various five-card holdings are given special names. a. how many 5 card poker hands contain two pair? Well I'm...

Hello everyone, another example in the book I'm wanting to make sure I'm seeing how they got their answer correctly. It says: Supppose the group pof 12 consists of 5 men and 7 women. How many 5 person teams contain at most one man? Solution: The set of teams containing at most one man...

Hello everyone im' stuck on this problem. It says: Each symbol in braille code is represened by a rectangular arrangement of six dots. Given that a least 1 dot of the 6 must be raised, how many symbols can be represented in brail? I'm thinking I have to use combinations becuase the...

I remember this from awhile back but can't seem to find any justification. Why is the smallest positive linear combination of two numbers necessarily the GCD of the two numbers?

I'm not sure where to start on this one at all, very confused. I don't want anyone to do the entire problem for me just point me in the right direction. I know how to compute probability from simple random events but this question just confuses the heck out of me :( Question: A labor...

Hi all, I am writing a course for budding engineers. I have been a marine engineer for long. While compiling my course I seem to have hit a roadblock that has made me aware of my ignorance in spite of my experience. I would like some help on this from anyone. I have classified diesel engines...

Linear combinations?? :S Hey, could som1 please explain linear combinations. I copied down the lecture notes but I'm not understanding this example :confused: may hav typo from the note takin Example: Show that each of the vectors w1 = (1, 0), w2= (0, 1) and w3 = (3, 3) are a linear...

i am given C(28,2n)/C(24,2n-4)=225/11 where C are combonations. i am supposed to solve for n. after subbing in n and k and simplifying i get (11*28!)/2n!=(225*24!)/(2n-4)! (i am pretty sure this is correct). i do not seem to be able to continue after that. how do i solve for n?

I am doing some work on high school (Australia) level combinatorics. So I've been taught nCr, nPr, and of course factorial (!). Now I need to apply the combinatorics to probability. There a two questions which I am stuck on. I calcualted that the sample space of all combinations was...

struggling with these problems: 1. determine if the following are: i) collinear: A(0, 3, 2), B(1, 5, 4) and C(3, 9, 8) ii) coplanar: A(1, 4, −5), B(2, 12, −8), C(4, 6, − 4) and D(5, 3, −2) i know that TWO vectors are collinear if it is possible to express one as a scalar multiple of the...

:cry: i need help solving problems involving selecting things. like for example find the number of ways in which a team of 3 men and 2 women can be selected from a group of 6 men and 5 women. im doing a retake of a statistics exam i did v badly in btw. i can't find any good websites about...

hello i need help solving problems involving selecting things. like for example find the number of ways in which a team of 3 men and 2 women can be selected from a group of 6 men and 5 women. :bugeye: i know how to do perms and combs but just don't know how to apply them.:eek: help...

Hi, I really need help with this question 1) the water depth in a harber is 21m at hight tide, and 11m at low tide. One cycle is completed approximatly every 12h. a) find an equation for the water depth as a function of the time, t hours, after low tide b) Draw a graph 48h after low...

One of the class objectives is to give an oral presentation to the professor. This time it has to do with explaining Permutations and Combinations. We have 4 things we need to explain: 1) Permutations / Repetitions are not allowed / Order Matters 2) Combinations / Repetitions are not...

The question is to write the following vectors as a linear combination: c) a vector directed at an angle of 45 degrees with a magnitude of square root of 2. d)a vector directed at an angle of 150 degrees with a magnitude of 6. What I tried to do is to find the scalar quantity with the...

From a deck of 52 cards, the 12 face cards are removed. From these face cards, 4 are chosen. How many combinations that have at least 2 queens are possible? The answer is 201... I can't get here. This is what I did: case1) 4 queens can be chosen C(4,2) ways * 10 cards can be chosen C(10,2)...

Four lattices are selected from 5*4 grid board indicated in the figure above so that they form the corners of a rectangle having sides parallel to the edges of the board. How many different rectangles can be formed in this way? Can anyone give me some clues to answer this question? Thanks:approve:

If 4 letters are selected from the 7 letters of the word "WINDOWS", calculate the number of possible a)combinations. b)arrangemants. I have got the answer but I still don't understand how to calculate it. Thanks.:rolleyes:

A manager has Rs.1000 from which he has to give a bonus to his five employees by following a condition that every employee must get atleast Rs.50 and every employee must be given integral amount of Rupees. in how many ways can he do it? Since them manager has to give Rs.1000 to...

You are taking a test with 10 questions, you only have to answer 7, how many ways are there to do it? 10 x 9 x 8 x 7 x 6 x 5 x 4 ? How many different ways are there to answer the questions if you must answer at least 3 from the first 5 questions? 5 x 4 x 3 x 7 x 6 x 5 x 4 ?

I was thinking that I could solve this with combinations. However, I am unsure of how to use it in this case. If I remember correctly, the combinations are given by: \begin{pmatrix}n \\ r\end{pmatrix}=\frac{n!}{r!\,\left(n-r\right)!} Hmm. Any thoughts on this? Am I on the right track...

Suppose I pick two number from {0,1,2} without replacement and suppose I keep track of which one was drawn first. This is a permutation question. There are 3!/(3-2)! = 6 possible permutations: (0,1) (0,2) (1,0) (1,2) (2,0) (2,1) Of course, if I only care which numbers were choosen, then I...

I have a problem that I'm not aware of how to solve. I know about permutations and combinations, but... Given that the possible values for a are all integers such that 2 \leq a \leq m_{a}, and the possible values for b are all integers such that 2 \leq b \leq m_{b}; how many combinations of...

Having a lot of trouble with a particular problem in the topic of variance. The problem is: "Suppose you are organizing a game where you charge players $2 to roll two dice and then you pay them the difference in scores. What is the variance in your profit from each game? If you are playing a...

If anyone is able to help me with this question regarding introductory Data Management, I would be grateful. Find the sum of all the five digit numbers that can be formed using the digits 1,2,3,4, and 5 without repeating any digit. Thank you! Artermis

I was just wondering how you would prove the following: \sum_{k=0}^{n}\frac{n!}{k!\left(n-k\right)!}=2^{n} Any help is appreciated.

In how many ways can 15 gifts be distributed equally: a) amongst Claire, Alana, and Kalena b) into three parcels of five gifts each For (a) I went _{15} P_{3}/3 = 910 I am 100% certain this is wrong. I also have no idea how to do (b). I would greatly appreciate any help on this...

Does an algorithm exist for generating a particular permutation of a combination? You just input the combination and the position of the permutation and it outputs the permutation.

In springs, when two springs are combined in series why is the total spring constant of the system 1/2k, and when three springs are combined in parallel, why is the total spring constant 3k?

Is it fair to say combinations are just an application of the counting principle? I already understand that permutations are just an application of fundamental principle and that combinations are just an application of permutations. If it's fair to say that combinations are in fact, just an...

Is it fair to say combinations are just an application of the counting principle? I already understand that permutations are just an application of fundamental principle and that combinations are just an application of permutations. If it's fair to say that combinations are in fact, just an...

I had mono while this unit was being taught so I am havin quite a lot of trouble figurin this homework out. Like this question: How many 6 digit numbers greater than 800 000 can be made from the digits 1, 1, 5, 5, 5, 8? I have absolutly no idea so any help would be appriciated! Thanks!

Ok, given a set: A How many distinct x tuples can be created using a subset of A? Example: |A| = 20 I want to know how many combinations of 7 tuples can be made from that set. Example: If A = {1 .. 20} three such combinations could be: {1, 2}, {3, 4}, {5, 6}, {7, 8}, {9, 10}...

What would be the best way to solve for n if 10Pn = 90? Also, how would you solve this problem: In a student council election, there are 3 candidates for president, 3 for secretary, and 2 for treasurer. Each student may vote for at least one position. How many ways can a ballot be marked...

Hi, I've been scratching around trying to figure out a formula for the following problem and I've got one that I think is correct. Just wondering if anyone can confirm it for certain (like maybe you have it in a textbook or know it well etc). Thanks. Problem : You need to partition n=k*m...

if there is lottery where there are six numbers of 49 drawn and each number is discarded one drawn what are the total combinations. I think it would be 49 choose 6 but that only gives 14 million and I figured it would be higher. can someone verify this? thanks :smile:

this is quite a classic problem i think but I am having difficulty finishing it off. If we have two stamps of positive values a and b, (greater than 1), what values can be expressed as a linear combination of these 2 stamps. If the stamps have a highest common factor greater than 1, then there...

How many 4 element subsets can you get from a 21 element set. I know the combination formula C(21,4)=5985. I was trying to see how this is working out though. I know there are 2^21 subsets of a 21 element set, I want to know how I can find the number of all the 4 element subsets without using...

How many combinations of three letters from the letters A,A,B,B,C,C,D are ther? ------------------------------ I assumed 2 cases: 1. 2 letters are the same. 2. all the 3 are different. And found 9 forms for the first case, and 24 for the second one. As you know my answer (33) is 20 more...

4 children out of 8 will be selected. But two oldest children can not be both chosen. Total number of combinations = ? The mutually exclusive situations are really confusing me. I know if they were independent, total n. of combinations would be \frac{8!}{(8-4)!4!}=70 I need to subtract...

How do u calculate the the total number of combinations, given that you have n number of object and you will choose r of the objects, but x of these objects are mutually exclusive. Let x=2 for your explanations. I kinda have an idea on how to do this, but i can't frecall an formula for the...

{1, x, x(x-1), x(x-1)(x-2)} you want to find the linear combinations that will give you 1, x, x^2, x^3 a + a(x) + a(x(x-1)) + a(x(x-1)(x-2)) = 1 a + a(x) + a(x(x-1)) + a(x(x-1)(x-2)) = x a + a(x) + a(x(x-1)) + a(x(x-1)(x-2)) = x^2 a + a(x) + a(x(x-1)) + a(x(x-1)(x-2)) = x^3 I don't...

I'm currently taking Physics in High School and having problems with Vectors. I apologize in advance if this is the wrong forum to post this on but here it is... I have to Diagram the vector combinations on graph paper and find the resultant and the equilibant. 3 N at 120(degrees)...

How exactly do you graph these? F(x) = 2x and G(x) = x + 1; Graph (F + G). Please help :\

All n-variable combinations can exist within a word; n=1 | a n=2 | ab n=3 | cabca Is the fourth shortest word cabdcabcdabcadbca, and how long is the n:th word?

i was wondering how to calculate the posibilities that a security code could be. For instance if a jet ski security code consists of 4 numbers. each digit can be any number 1 through 5. how many combinations can that make? p.s. - I am not trying to steal a jet ski; I am just wondering.

I got this two problems, I can't figure them out... A bookshelf contains m different books and n copies of each. How many different selections can be made from them? and In how many different ways can four letters be posted in four envelopes so that no one receives the correct letter?

How many ways can you select four letters out of the word parallelogram ? The answer on the book is 150. For me I am stuck at using 8C4 and it seems to be the logical way. The reason I chose 8 is because some letters are repeating. So how can they have 150?