Permutation Definition and 276 Threads

Homework Statement There are 30 students in a class. In how many ways can we arrange them if : a)we must have three group, group one must have 5 students , group two 10 students and group three 15 students. answer=\frac{30!}{5!*10!*15!} b)we must have three group and all must have 10 students...

Homework Statement From the numbers 4,5,6,8,9 we make 5 digits numbers (each number can be used only once). h)How many of these numbers are divisible by 8? The correct answer is 20 Homework Equations a number is divisible by 8 if the last 3 digits are divisible by 8 If the hundreds digit is...

Homework Statement so for a side task I'm supposed to assign people to groups for an icebreaker in python, can anyone give me links to theories that I could read up on or give me suggestion X number of people at my company signed up for a dinner roulette as a way to meet new people. Everyone...

Homework Statement From 5 consonants and 4 vowels, how many words can be formed consisting of 3 consonants and 2 vowels The book solved it using combination C(5,3) * C(4,2) * 5! = 7200 i.e I understand the 1st two term give the unique 5 words that can be formed with 5 consonants and 4 vowels...

Homework Statement Six cards and six envelopes are numbered 1,2,3,4,5,6 and cards are to be placed in envelopes so that each envelope contains exactly one card and no card is placed in the envelope bearing the same number and moreover the card numbered 1 is always placed in envelope numbered 2...

Homework Statement Proove that... (AxB)x(CxD)=(A.BxD)C-(A.BxC)D=(A.CxD)B-(B.CxD)A using Permutation Symbols Homework EquationsThe Attempt at a Solution I am confused about what to do after the third line from 'vela's response' (Post #2 from the reference link below). Reference...

How many 7-digit numbers can be formed from the digits 1, 1, 2, 2, 4, 4 and 5 if repetition is not allowed. If one of these numbers is chosen at random, find the probability that it is(a) greater than 4,000,000(b) even number and greater than 4,000,000 Question b is so confusing . Help me

N is a 2 x n matrix: N = 1 2 3 4 ... n-1 n n n-1 ... 4 3 2 1 then N^2 = 1 2 3 4 ... n-1 n 1 2 3 4 ... n-1 nYou COULD use the theorem: sgn(N^2) = sgn(N)sgn(N) however, I am asked to find sgn(N^2) by the traditional method: sgn(N^2) = (-1)^([L1 - 1] + [L2 - 1]...) where L represents the...

say i have the matrix (4,2,5,6,3,1) and on top I have (1,2,3,4,5,6) i.e. a 2x6 permutation matrix. Let's call it sigma. how would I calculate (sigma)^2? I can break it down into cycles: sigma = <1,4,6>compose<3,5> thanks.

I am doing some self study of groups and can solve problem #3 but not Problem #4. Problem 3. Let A be a finite set, and B a subset of A. Let G be the subset of S_A consisting of all of the permutations f of A such that f(x) is in B for every x in B. Prove that G is a subgroup of S_A. Problem...

Hey guys, there's these questions in my hm that's really tough for me and i basically have no clue on how to do it. Any help is greatly appreciated 1.a) Give the numbers 1,1,2,3,4,5,5,6,7, If five numbers are randomly selected without replacement, how many different numbers can be formed if...

Homework Statement In how many ways can one choose 6 cards from a normal deck of cards so as to have all suits present?Homework EquationsThe Attempt at a Solution 4 different cards can be chosen in 13*13*13*13 ways. Now we have to choose 2 remaining cards from 48 cards. This can be done in...

Homework Statement On his university application, Prashad must list his course choices in order of preference. He must choose four of the six courses available in his major discipline and three of the four courses offered in related subjects. In how many ways can Prashad list his course...

Homework Statement This is my first exposure to Einstein notation and I'm not sure if I'm understanding it entirely. Also I added this class after my instructor had already lectured about the topic and largely had to teach myself, so I ask for your patience in advance... The question is...

I'm asked to show that a permutation is even if and only if the number of cycles of even length is even. (And also the odd case) I'm having trouble getting started on this proof because the only definitions of parity of a permutation I can find are essentially this theorem. And obviously I...

Homework Statement Prove that there is a permutation sigma, such that sigma * (1 2 3) * sigma inverse= (4 5 6). Homework Equations The Attempt at a Solution I know that since the order of the two cycles is the same there must be a sigma such that the two permutations are equal but I...

Homework Statement Hi, I have been MIA lately due to work, but I am back with questions, and eager to learn! I am self studying, and so I have inconsistencies in my learning which I hope to iron out. Suppose you are told that the permutation ( 1 2 3 4 5 6 7 8 9 3 1 2 X Y 7 8 9 6) In S9...

Homework Statement a) How many different initials can someone have if a person has at least two, but no more than five, initials? You may assume that each initial is one of the 26 uppercase letters of English, and that letters can be repeated. b) When attempting to name his son, Jor El...

Homework Statement A security code is formed by using three alphabet and four digits chosen from alphabet {a,b,c,d,e} and digits {1,2,3,4,5,6}. All digits and alphabets can only be used once. Find the number of different ways the security code can be formed if (a) there is no restriction...

Homework Statement Find the sign of the permutation --> Picture here: http://tinypic.com/view.php?pic=2q8rkso&s=5 No other given data. Homework Equations ε(σ) = (-1)^m(σ). If i < j and σ(i) > σ(j) then there's an inversion. Where ε(σ) denotes the sign of the permutation and m(σ) the number of...

Reviewing for my final exam can anyone please help access these problems? a) How many ways can 11 football players stand in a circular huddle? I put 11P11 b) 12 identical laptops are in the inventory of a dealer, and 2 have hidden defects. If 5 computers to be shipped are selected at random...

Hello, I would like to check if the work I have done for this problem is valid and accurate. Any input would be appreciated. Thank you. **Problem statement:** Let $G$ be a group of order 150. Let $H$ be a subgroup of $G$ of order 25. Consider the action of $G$ on $G/H$ by left...

I am having trouble proving that my function is surjective. Here is the problem statement: Problem statement: Let T be the tetrahedral rotation group. Use a suitable action of T on some set, and the permutation representation of this action, to show that T is isomorphic to a subgroup of $S_4$...

Homework Statement How many necklace with 5 white beads and 5 black beads can be constructed? Homework Equations Circular Permutation problem The Attempt at a Solution] I did 10!/5!5!=252 but from there I didn't get anywhere. I know this includes repeats from rotational...

It's a permutation question, so I don't know where else to post this. How many eight digit even numbers are possible with the digits 7 5 4 5 7 5 0 7? Please explain step by step.

How can I prove that, for N\gg n \frac{N!}{(N-n)!}\approx N^{n} I've tried doing \frac{N!}{(N-n)!}=\exp\left(\ln\frac{N!}{(N-n)!}\right)=\exp\left(\ln N!-\ln\left(N-n\right)!\right) \underset{stirling}{\approx}\exp\left(N\ln N-N-\left(N-n\right)\ln\left(N-n\right)+N-n\right)...

Hello folks, I'm not even sure if this is the place to put this but with some luck it might be. I just have a general question about permutations. I understand the concept of even and odd permutations of a set of numbers, what I am hoping for is an easy way to figure out if (given a...

I couldn't find the words to summarize my question perfectly in the title so I will clarify my question here. Say we have a group G in which every element can be written in the form g_1^{e_1} g_2^{e_2}...g_n^{e_n}, 0 ≤ e_i < |g_i| . Suppose that there exists a different set g_1', g_2', ...

Homework Statement There are 2n points on a circle, we want to connect each two of them to make a pattern of connection in the way that there is no cross between the lines of connection, and all the lines have to be inside the circle and on the plane of the circle. Question: How many different...

[b]1. Prove the following identity: Ʃ(n choose k)(m-n choose n-k) = (m choose n) from k = 0 to k = n I've tried induction, and just played around with a few properties of permutations, but nothing seems to satisfy the proof, any ideas?

Homework Statement A notorious postman delivered 4 letters to four houses in such a way that no house will get the correct letter...in how many ways he delivered the letter ? Please explain it Homework Equations I think this is permutation question...using fundamental law of counting...

Total no. of permutation of the words $\bf{PERMUTATIONS}$ in which there are exactly $4$ letters between $P$ and $S$, is My TRY:: If we fixed $P$ and $S$, Then there are $10$ letters $\bf{ERMUTATIONS}$ out of $10$, we have to select $4$ letters of $4$ gap b/w $P$ and $S$ and then arrange in...

Hi everyone, I have a problem I'm trying to solve. If anybody can help it would be greatly appreciated. (PS: My understanding of maths is so poor I don't even understand the meaning of half the forum titles so please excuse me if I've posted in the wrong section..!) All the possible 2...

Homework Statement Note: I need help with part (c). Consider the representation P: S_3 \rightarrow GL_3 where P_{\sigma} is the permutation matrix associated to \sigma. a) Determine the character \chi_P : S_3 \rightarrow \mathbb{C} b) Find all the irreducible representations of S_3. c)...

Homework Statement Supposing P is a permutation matrix, I have to show that PT(I+P) = (I+P)T. Is there any general form of a permutation matrix I should use here as permutation matrices of a dimension can come in various forms. Homework Equations The Attempt at a Solution I did...

For example, how to obtain E_(yz,xz)(l,m,n) from E_(xy,xz)(l,m,n)?

Homework Statement The total number of ways in which 5 balls of different colours can be distributed among 3 persons so that each person gets at least one ball is ... Homework Equations The Attempt at a Solution I began by finding the number of ways of distributing 5 balls among...

How many numbers of 6 digits which have exatctly the digit 1 (2 times), digit 2 (2 times), without zero, are there? The book post this solution: \frac{6!}{2!2!}*\binom{7}{2} + \frac{6!}{2!2!2!}*7= 4410, but I'm trying to find an explanation for this result.

Does the permutation group $S_8$ contain elements of order $14$?My answer: If $\sigma =\alpha \beta$ where $\alpha$ and $\beta$ are disjoint cycles, then $|\sigma|=lcm(|\alpha|, |\beta|)$ . Therefore the only possible disjoint cycle decompositions for a permutation $\sigma \in S_8$ with...

Homework Statement If three different number are taken from the set {0, 1, 3, 5, 7} to be used as the coefficient of a standard quadratic equation, how many such quadratic equations can be formed? How many of these have real roots?Homework Equations The Attempt at a Solution Part a: "How many...

Homework Statement So, you have a dial with 12 numbers (1 through 12), and you're wondering how many ways can you connect an number to another. So its therefor asking how many lines can you make with 1 - 12 in a circle. Homework Equations The Attempt at a Solution I got the...

what is the permutation? and like what example? anyone knows?

Homework Statement http://i49.tinypic.com/wmmhbl.png Homework Equations The Attempt at a Solution my answers : Q1:(a) (i) 8! (ii) 4!*5! Q1:(b) 7P3*5P2 Q2: 4320 ways Q3: 12!*3! Are my answers correct?

Homework Statement http://i49.tinypic.com/2hoeghs.png Homework Equations The Attempt at a Solution (i) 144 ways (ii) 2!*4!*3! (iii) 12*5! these are my answers

This is NOT homework. This is a personal project I am working on. First and foremost, THANK YOU in advance for helping me with my statistics project that I have been unable to solve on my own or through the help of my statistics book and google. I am working on an excel spreadsheet for use...

Homework Statement How many different six-digit numbers are there whose three digits are even and three digits are odd? Homework Equations No equations are required.We only need the principles of counting. The Attempt at a Solution I tried to split into 4 cases: case I:there is...

Question: Six mobsters have arrived at the theater for the premiere of the film “Goodbuddies.” One of the mobsters, Frankie, is an informer, and he's afraid that another member of his crew, Joey, is on to him. Frankie, wanting to keep Joey in his sights, insists upon standing behind Joey in...

Right I am having an issue with the proof to permutation, I really can see the n-r-1 I think the confusion stems because it is in the general term, which throws me a bit, if possible could someone maybe write it in numbers and the underneath write in the general term if not too much trouble. The...

There are three separate bundles of reading material comprising of 4 comics, 2 novels and 3 magazines. They are placed together to form one pile. In how many ways can this be done if there are no restrictions on where the individual items are to be placed? I say 9! = 362880 Determine the...

Homework Statement See image. Homework Equations The Attempt at a Solution I am finding the orders of permutations. I know that you first find the orbits or cycles I don't know the difference (but I should). This is what my professor said: If you have (1345)(897)...