Permutations Definition and 287 Threads

Homework Statement Board of directors has 10 members. from the 10 members they will elect 5 officers. President, vice-pres, sec and treas A) From the 10 board members how many combinations of officers are there? B) If three board memebers are physicians, how many combinations have a physician...

Homework Statement Let α = (α1α2...αs) be a cycle, for positive integers α1α2...αs. Let π be any permutation that παπ-1 is the cycle (π(α1)πα2...π(αs)). Homework EquationsThe Attempt at a Solution I started by choosing a specific α and π, and tried finding παπ-1 to give myself some idea of...

Homework Statement Consider a 11 digit positive integer formed by the digits 1,0 or both. The probability that no two zeros are adjacent is: Homework Equations None The Attempt at a Solution First digit has to be 1. Total number of permutations=210 Now 1XXXXXXXXXX is the format. Taking 10...

Having problems with question 9 and what I came up was Case 1: 1st person gets 1 And 2nd person gets 3 OR Case 2: 1st person gets 3 And 2nd person gets 1 OR Case 3 They both get 2 And seeing that they are both dependent events so that once a person receives an article it affects the...

Find 'n' using permutations: 1/4! + 1/5! + 1/6! = n/7!

Homework Statement In the text, the products pq and qp of the permutations (2 3 4) and (1 3 5) were seen to be different. However, both products turned out to be 3-cycles. Is this an accident? Homework Equations p=(3 4 1)(2 5) q=(1 4 5 2) where p and q are permutations The Attempt at a...

We're currently studying counting and the different equations which are the foundation of probability (permutations and combinations). I understand that permutations are used when order is taken into account and combinations is for when order doesn't matter. However, the two equations appear...

I was going through a p and c problem where I had to find the number of non congruent RECTANGLES. Answer includes number of squares as well. SHOULD SQUARE BE TAKEN AS A RECTANGLE?

How many permutations of 4 letters can be made out of the letters of the word 'examination'?

Homework Statement The total number of ways in which 5 balls of different colors can be distributed among 3 persons so that each person gets at least one ball is Ans: 150Homework EquationsThe Attempt at a Solution I don't understand what's wrong with my answer. In case of each person getting...

Homework Statement In how many ways can m men and n women be arranged such that no two women are besides each other? (m > n)Homework EquationsThe Attempt at a Solution The given answer is m! x P(m + 1, n). I understood how the answer should be a multiple of m!. I also understood that there...

With 6 red, 3 blue and 3 green flower pots, how many color permutations in row of 12 are there ? Its not 12! or n!/(n-r)!

Alan F beardon, Algebra and Geometry chapter 1 6. For any two sets A and B the symmetric difference AΔB of A and B is the set of elements in exactly one of A and B; thus AΔB = {x ∈ A ∪ B : x / ∈ A ∩ B} = (A ∪ B)\(A ∩ B) . Let be a non-empty set and let G be the set of subsets of (note that G...

Homework Statement "A 3-digit number is made up using the digits 0, 1, 2, 3, 4, 5, 6 and 7 at most once each. The number cannot start with 0. How many such numbers can be formed if: a. there are no other restrictions b. the number ends in a 5 c. the number ends in a 0 d. the number is...

Homework Statement If k is moved by σ, then σk is also moved by σ proof: otherwise σk is fixed by σ, that is σ(σk) = σk. But the fact that σ is one-to-one gives σk = k, which is contrary to the hypothesis. I am confused trying to understand this. I don't understand the part that says...

Dear all, Please read the text in the attachment. Then... 1)Explain what is meant by "fix k" and "fixed point of ρ" ? 1a) What does ρ(k) = k mean? 2) How to make the permutation of αβ? 3) What does "re-arranging α so that its top row coincides with the bottom row of β, and...

Homework Statement In how many ways is it possible to select one or more letters from those in INSIPIDITY? Homework Equations The Attempt at a Solution My initial impression was that this was a combinations problem and I did not have to take into account the repetitions. This led...

Hello everyone, I am an aspiring math teacher taking a workshop type class and in two weeks my group will be teaching the other students various topics on probability. We are trying to come up with a fun and interactive way to teach the counting principle, permutations, and combinations. To...

is there any easier way of proving that no matter how an identical permutation say (e) is written the number of transpositins is even. my work i tried let t_1...t_n be m transpositions then try to prove that e can be rewritten as a product of m-2transpositions. i had x be any numeral appearing...

Homework Statement Theorem 8.1 of Dan Saracino: Let f ε S_{n}. Then there exist disjoint cycles f_{1},f_{2} .. in S such that f= f_{1}°f_{2}... In proving this theorem, it considers a finite group S_n={1,2,..,n} and chooses x_1 ε S_n. Then it defines x_2= f(x_1), x_3=f(x_2) and so on. The...

Hello, today in class we started a topic on permutations and combinations and I have come across a way in which it could be of use to me whilst working with 'logictutor' (a premade circuit board used to teach simple logic circuits). We have an experiment tomorrow where we will investigate...

Homework Statement Suppose σ is an element of S_n, if σ^5=1, is σ necessarily odd or even Homework Equations Parity(\sigma)= (\sum_{i=1}^k(|c_i|-1)) mod 2 The Attempt at a Solution Really unsure how to even start this, I think I have to use the fact you can decompose every...

Is there a theorem or any useful application for knowing the order of a permutation belonging to the symmetric group Sn? For example, Lets say σ is a permutation belonging to S5; i.e. σ is a permutation of {1,2,3,4,5}. If we are given that σ^7 = I (the identity permutation), then how can we...

Reviewing for finals and got this question wrong: How many different permutations are there of the letters in the word LOLLIPOP what I did was 8P8, how would you solve this?

First of all, I would like to apologize for my bad english. The Problem: There is n members inclusive CEO and 2 vice presidents. In how many ways can they be seated around a table so that both vice presidents sits next to the CEO?Attempt at a solution: There's in total (n+2)! ways to be...

http://dwite.ca/questions/haunted_house.html So this is from a contest I wrote a while back, I took the greedy approach for my solution, and I did get 5/5, but my solution was not totally correct because the shortest path was not guaranteed, if a candy was 2 spaces before the start, and a...

Suppose I was asked if G \cong H \times G/H . At first I considered a familiar group, G = S_3 with its subgroup H = A_3 . I know that the quotient group is the cosets of H, but then I realized that I have no idea how to interpret a Cartesian product of any type of set with elements that aren't...

Homework Statement Lets say a car plate has 6 positions, three of them are numbers and 3 of them are alphabetic. e.g. ABC 123. I need to figure out how many possible permutations can occur using all the numbers and alphabets BUT i cannot use any number or alfabet twice in an permutation eg...

Here are the questions: I have posted a link there to this topic so the OP can see my work.

So the general formula for permutations as I understand it is n!/(n-k)! but what if n=k? so let's say you want to see how many ways you can seat 5 people in 5 chairs. then the answer would be 5!/(5-5)! which would be undefined...but logically it should be defined what did I...

Homework Statement 8. Using the digits 1, 2, 3, 5, 7, 8 how many 4 digit numbers greater than 5,364 could be constructed if: a) Repetition of the digits is allowed? b) Repetition of the digits is not allowed?Homework Equations The Attempt at a Solution for part a: 2*6*6*6 (for 8 and 7 as the...

Homework Statement The coach from a soccer team of 15 players must select 11 players for the start of a game. ) Before the game all players line up in a straight line for a team photograph. If 2 players, Michaela and Aleah must be together, then how many different arrangements can be made for...

I have trouble using isomorphism and permutation in proofs for combinatorics. I don't know when I can assume "without loss of generality". What are some guidelines to using symmetry in arguments. One problem I'm working on that uses symmetry is to "prove that any (7, 7, 4, 4, 2)-designs must be...

It's been a while since I've posted. This is a problem I had for a homework assignment a few weeks ago but I completely figure out. Any help appreciated. Homework Statement "A card-shuffling machine always rearranges cards in the same way relative to the order in which they were given to...

Homework Statement I have n elements, of which I take x and arrange them, with repetitions allowed (i.e. if one of my elements is A, and x=3, then {A,A,A} would be an acceptable permutation). Among the original n elements is the letter A, present a times, and the letter B, present b times; of...

The theory says that if you have x objects containing a repeats of one element and b repeats of another, Np(without repetition)=x!/(a!b!). If you have x objects and repetitions are allowed, Np(with repetition)=xx, correct? Combining these, if we have x objects containing a repeats of one...

Homework Statement 1.) 4 of the books have red covers, 3 have green covers, and another 2 have gray covers. In how many ways can the books be arranged on a shelf if books of the same color must be arranged together? The Attempt at a Solution 1) I think that the answer here is 3...

Hi all, I've answered a question but there's no answer for it, and if ye could tell me if I'm doing it right I'd appreciate it thanks :) Permutation: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 --------------------2 3 1 6 5 4 8 10 13 11 12 7 14 9 (i) Write it as a product of transpositions. I...

Homework Statement How many ways can a boat crew of 8 women be arranged if 3 of the women can only row on the bow side and 2 can only row on the stroke side?Homework Equations The Attempt at a Solution I simply did 8!/5! (5!/3!)3! which is simply 3!(8!/3!) The correct answer is 1728.

So, (this is not homework), I have been stuck on a question regarding probability for a while now and am clueless of how to continue. The question is: The letters A, E, I, P, Q, and R are arranged in a circle. Find the probability that at least 2 vowels are next to one another. My attempt...

Hey guys, I have a problem relating to combinations and permutations.In how many ways can I divide a deck of 52 cards into piles of 3 with each pile containing any number? for example 50,1,1 or 45,6,1 Thanks in advance

Hi, here's the question, I just need someone to confirm that I'm doing it right (been a while since my last stat class): Let's say I have 30 balls all of different colors. I want to know in how many different ways I can align 5 balls picked at random (thus ordering matters). Note that one...

Hi, here's the question, I just need someone to confirm that I'm doing it right (been a while since my last stat class): Let's say I have 30 balls all of different colors. I want to know in how many different ways I can align 5 balls picked at random (thus ordering matters). Note that one...

Homework Statement In how many ways can the three letters from the word " GREEN " be arranged in a row if atleast one of the letters is "E" Homework Equations Permutations Formula The Attempt at a Solution The total arrangements without restriction: 5P3/2! = \frac{5!}{2! * 2!} The number...

Say we have the symmetric group S_5. The permutations of \{2,5\} are the identity e and the transposition (25). But what are all the permutations of \{3\}? Is it e and the 1-cycle (3)?

Homework Statement In a polygon , no three diagonals are concurrent. If the total number of points of intersection of diagonals interior to the polygon be 70 , then find the number of diagonals of the polygon. (You must get a numerical value..) Homework Equations Number of diagonals...

Questions regarding "permutations". Homework Statement These two mini questions , I think , can be adjusted in one thread itself. 1. How many total 5-digit numbers divisible by 6 can be formed using 0,1,2,3,4,5 if repetition of digits is not allowed ? 2. In the decimal system of...

Homework Statement 1.How many 4 digit even numbers greater than 5000 can you form using the digits 0,1,2,3,5,6,8 and 9 without repetitions? How do i go about this? b) how many of these numbers end in 0? 2. n_P_3=120 3. How many ways can all the letters of aloha be arranged if each...

Homework Statement This is not really a question. More of an understanding issue. They have created a table for the alternating group of degree 4 in my book and I'm having trouble understanding it. http://gyazo.com/87980bef3669619796dda2f55a9d04d1 Homework Equations Cycle notation...

Homework Statement How many "words" with 5 letters can be created from the letters in the word ALGEBRA? Each letter can be used only once. Homework Equations The Attempt at a Solution I know the answer to this (1320) and I know how I got to it (which I'll describe in a minute)...