Permutations Definition and 287 Threads

I'm pretty sure I'm right, but I'd appreciate it if I could obtain some verification. Homework Statement Consider the following grid: The goal is to move from point \alpha to point \beta to point \gamma by moving along the edges of the grid from point to point. You can only move to the...

Hi all I am new , and wanted to ask the following. I do not know if this is the right section but here goes: I have three registers , say A , B and C Case 1:A will always have 3 combinations 1,2,3 1 has further subsections 1_1,1_2,1_3,1_4,1_5 2 has further subsections 2_1,2_2,2_3 3...

Alright, I understand what a stabilizer is in a group, and I know how to find the permutations of An for any small integer n, but for a stabilizer, since it just maps every element to 1, would all permutations just be (1 2) (1 3) ... (1 n) for An?

Homework Statement How many elements of each cycle-type are there in S5? The Attempt at a Solution One way of working this out would be to write out each permutation and see how many 2-cycles, 3-cycles ,4-cycles and 5-cycles there are but given that there are 5! permutations this would...

Well I am coming across problems like finding permutation of some n characters. On paper I can find all the permutations given some finite characters easily but when it comes to programming it is hard, why? Why is it hard to tell a computer what I myself can do it so easily? This is strange -...

How can I solve this? Find the value of n.1. P(n,2)=90 ; 2. P(n,3)=3P(n,2) I tried like this but I am stuck 1. n! / (n-2)! = 90 and then I don't know ... 2. n!/(n-3!) = 3 n!/(n-2)! ⇔ n! (n-2)! / (n-3)! n! = 3 ⇔ (n-2)! / (n-3)! = 3 here the same As you can see I'm really stuck with this.

In my statistics class I am making use of permutations very often. I need to make sure I understand this. If I have a set of 13 elements, I can arrange that 13! different ways, because Psub(13,13) = 13!/0!. If I pick 2 elements from those 13 elements, I can get 13!/11! different results...

How many permutation of the letters of the words $\bf{"MADHUBANI"}$ do not begin with $\bf{M}$ but end with $\bf{I}$

Hello I have recently come across a problem in my programming exercises that I haven't been able to solve, even after several days of hard thinking and tinkering. I have found that this problem may be solved by means of permutations using factorials, but there is a specific permutation...

Hi all, I have a set of questions, with answers in brackets at the end of each of them. I really don't know how to solve them, and have spent a whole morning trying to figure them out. Please help me! (answer one/all of them!) 1. In a game of chance, each player throws two unbiased dice and...

I am having trouble understanding the permutations of a finite set in general. I want to know what it may be used for, and how to solve some of its problems (examples?). In my attachment, I post some pictures of what I am currently reading, and what has confused me.

Hi, I have a terrible time understanding one of the concepts in the following question: How many 7 persons committees consisting of 4 females and 3 males may be assembled from a pool of 17 females and 12 males. Ok, so I get this is a combination question. Splitting this between male...

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...

Just need to learn how to use permutations in this question How many integers between 100 and 150 have three different digits in increasing order. One such is 147. I solved this using a long and unnecessary method. Can anyone guide me in how to solve it using permutations. I got 18 as...

Homework Statement Prove: If σ is a cycle of odd length, then σ2 is a cycle. Homework Equations N/A The Attempt at a Solution Proof: Assume σ is a cycle of odd length. Then let us model σ as (1 2 3 4 ... 2k +1) for some integer k [assuming here that the fixed elements of σ are...

hey guys, I just want grasp the whole concept of quotient groups, I understand say, D8/K where K={1,a2} I can see the quotient group pretty clearly without much trouble however I start to get stuck when working with larger groups, say S4 For instance S4/L where L is the...

Homework Statement How many eight-digit numbers can be formed under each condition? a) The leading digit cannot be zero, the fifth digit cannot be 6 or 8, and the number must be less then 75,000,000. b) The leading digit cannot be zero, the number must be divisible by 5, the fourth digit...

Homework Statement Please see attached image. Homework Equations The Attempt at a Solution I don't understand the problem at all. Can someone explain to me what the problem is stating, more precisely what an arrangement is? An example would be nice. Thanks.

Homework Statement Let X and Y be finite nonempty sets, |X|=m, |Y|=n≤m. Let f(n, m) denote the number of partitions of X into n subsets. Prove that the number of surjective functions X→Y is n!*f(n,m). Homework Equations I know a function is onto if and only if every element of Y is mapped...

Homework Statement The problem says to compute the expression shown for the permutations σ, τ, and μ. My problem in particular says to compute |{σ}| for σ= (1 2 3 4 5 6; 3 1 4 5 6 2) The Attempt at a Solution My attempt to solve this problem was by first trying to change σ into σ^2...

Hi, I have the following questions 1) A coin is tossed 9 times. In how many ways could the results be six heads and three tails? 2) A man bought two vanilla ice cream cones, three chocolate ones, four strawberry, and one butterscotch. In how many ways could he distribute them among his 10...

I am trying to create a mathematical model from a table of possible permutations. The table essentially consists of a list of various combinations of variables (there are 7 of them) and then an education guesstimate of how long that combination would take. Each variable is restricted to a...

Hi there, I'm doing homework right now (no this isn't a homework question!) and have basic questions on permutations and cycles. The concept seemed so simple in class and still seems simple, but the notation using lowercase Greek letters is confusing me. Do η and \theta and most of the...

So if I have numbers 1,2,3, intuitively you can say that there are 6 permutations: 123 132 213 231 312 321 If there any way to rigorously prove that these are the only possible arrangements of these three numbers? Even more simple, is there any way to prove that 12 and 21 are the only...

Hi, Homework Statement Can all permutations of {A,B,C,D} be made by multiplications of transpositions (AB), (BC), (CD)? And by multiplications of transpostion (AB) and 4-cycle (ABCD)? What is the maximum number of multiplications needed in both cases? Homework Equations All...

Homework Statement I am stuck on this problem relating to permutations: The first part asks how many ways can 6 people be lined up. This answer, I believe is 6! = 720 ways. The second part: If 3 specific persons, among 6, insist on following each other, how many ways are possible...

Homework Statement A telephone extension has four digits, how many different extensions are there with no repeated digits, if the first digit cannot be zero? Homework Equations P(n,r)=n!/(n-r)! The Attempt at a Solution For the first digit, there are 9 possibilities (because no...

Ok, so obviously, given some polynomial P(x) of degree r, it has r roots in the complex numbers by the FTOA, and if these roots are u_1, u_2,... it can be written as \begin{array}{l} P(x) = (x - {u_1})(x - {u_2})(x - {u_3}) \cdots \\ P(x) = {x^r} - ({u_1} + {u_2} + {u_3} + \ldots ){x^{r - 1}}...

Homework Statement Let s*(f) be the minimum number of transpositions of adjacent elements needed to transform the permutation f to the identity permutation. Prove that the maximum value of s*(f) over permutations of [n] is {n \choose 2}. Explain how to determine s*(f) by examining f...

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 Suppose x_{1} = \begin{pmatrix} 2 & 9 & 6 \\ \end{pmatrix}\begin{pmatrix} 3 & 5 & 8 \\ \end{pmatrix}\begin{pmatrix} 4 & 7 \\ \end{pmatrix} and x_{2} = \begin{pmatrix} 1 & 5 & 9 \\ \end{pmatrix}\begin{pmatrix} 2 & 7 & 6 \\ \end{pmatrix}\begin{pmatrix} 3 & 4 \\...

Homework Statement Suppose A = (a1 a2 . . . ak) and B = (b1 b2 . . . bk) are two cycles of length k. Find a permutation C, such that CAC-1. Next, suppose A and B have the same cycle structure. The question is again the same. Find a permutation C, such that CAC-1. The Attempt at a Solution...

Homework Statement In a finite group, show that the number of nonidentity elements that satisfy the equation x^5=e is a multiple of 4. If the stipulation that the group is finite is omitted, what can you say about the number of nonidentity elements that satisfy the equation x^5=e? Homework...

Homework Statement Michelle knows that there are 8!/2!2! permutations of her name when ALL the letters are used. She would like to know how many permutations there are if ANY NUMBER OF LETTERS in her name are used. Explain your procedure. The Attempt at a Solution this is what i figured...

Homework Statement A is a subset of R and G is a set of permutations of A. Show that G is a subgroup of S_A (the group of all permutations of A). Write the table of G. Onto the actual problem: A is the set of all nonzero real numbers. G={e,f,g,h} where e is the identity element...

Say I have three elements: A, B, C. I can list all the permutations by going alphabetical in the first element, then the second, then the third, and so on, like so: ABC ACB BAC BCA CAB CBA What I'm wondering, is given a number N, how do I decompose this into knowing what permutation it...

Homework Statement Consider the group of permutation on the set {123}. Is this group cyclic? Justify your answer Homework Equations The Attempt at a Solution I wrote out the cayley table for this group, and noticed that if we take (123)^3 = e . Seeing as we can get back to the...

Permutation...need help... I don't get the permutation problem about phone numbers...where i can use the same number for several times...or how to put letters in postbox..where i can put all the letters in only one postbox...can anyone explain the general rule and ideas of this kind of...

When composing permutations in group theory I don't know how to proceed. The way I see it there are two possible methods: assigning labels to the moving particles (e.g. "1" moves around the rhombus),or assigning labels to their starting positions (e.g. "1" is always the current particle at the...

I'm trying to figure out a problem at work. Last year my company sent out 6 pieces of direct mail. A person could have received any combination of 1-6 (received only #1, received #2,5,6, #1-6, etc.). They also could have responded to only one of them, but obviously had to receive the one...

Homework Statement The number of ways in which 4 distinct balls can be kept in 7 different boxes if each box can have atmost 1 ball are?The Attempt at a Solution Easy one but I need to verify my answer. The first ball can be kept in any of the 7 boxes in 7 ways The second ball can be kept in...

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 List the elements of the cyclic subgroup of S_6 generated by f = \left(\begin{array}{llllll} 1 & 2 & 3 & 4 & 5 & 6\\ 2 & 3 & 4 & 1 & 6 & 5\\ \end{array}\right)Homework Equations The Attempt at a Solution I really do not understand what the elements of a permutation really...

Homework Statement Given Information: If sigma is a permutation of a set A, we say sigma moves "a" in set A iff sigma("a") is not equal to "a". For the symmetric group S_36 of all permutations of 36 elements, let H be a subset of S_36 containing all permutations that move no more than for...

Homework Statement How many permutations of the letters a, b, c, d, e, f, g have either two or three letters between a and b? b _ _ a is also very much possible.Homework Equations nPr= n!/(n - r)!, where n >= rThe Attempt at a Solution For this question there can be 4 cases which are as...

Homework Statement Find the permutations that correspond to the rigid motions of a rectangle that is not a square. Do the same for the rigid motions of a rhombus that is not a square. Homework Equations The Attempt at a Solution I began by drawing the rectangle and rhombus and...

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 In how many ways can 3 balls of different colours be put in 4 glass cylinders of equal width such that any glass cylinder may have either 0,1,2 or 3 balls? The Attempt at a Solution Using the formula for no. of ways for distribution of n distinct things into r...

First I'd like to mention I don't want the answer, I'd just like a hint in the direction which I should start working in. I just don't know how to begin the problem. Homework Statement How many permutations of 1, 2, . . . , n are there in which i is never immediately followed by i + 1, i = 1...