Permutations Definition and 287 Threads

i was wondering if anyone can help me understand why the product of two odd permutations is odd? i came across this on a website but it didn't help me understand why. thanks for the help

I just want to ask if my work is correct... This are the questions: 1. In how many ways can the letters of MISSISSAUGA be arranged? -->6*6*6*6*6*6*6*6*6*6*6 = 362,797,056 2. A man bought two vanilla ice creams, three chocolate cones, four strawberry cones and maple walnut cone for his 10...

i just want to ask if my answer is correct... the problems is ... how many numbers greater than 300 000 are there using only the digits 1,1,1,2,2,3? my answer is... 1(three)*5(the position)*2(the numbers 1 and 2) = 10 therefore, the numbers greater than 300 000 is 10 is this right...

i cannot get the question since i don't know how to play baseball... this is the question... The manager of a baseball team has picked the nine players for the starting lineup. In how many ways can he set the batting order so that the pitcher bats last? im just guessing, is this correct...

i cannot get the question since i don't know how to play baseball... this is the question... The manager of a baseball team has picked the nine players for the starting lineup. In how many ways canhe set the batting order so that the pitcher bats last?

Hi, I need to work out the number of all permutations, \tau, in the form: \tau = (\sigma_1 \sigma_2 \ldots \sigma_n) (\theta_1 \theta_2 \ldots \theta_n) \quad \text{for} \quad \sigma_i \neq \theta_j \quad \text{and} \quad \tau \in S_{2n} Namely 2 disjoint cycles of equal length in the...

Ok, for some reason my answers for the following 3 questions we were given for homework on permutations are wrong (according to the answers in the back of the text). I was hoping that somebody could point me in the right direction, these basic ones should be simple for me. Thanks! In how...

The prime ministers A, B, C, D, E, F and G of 7 countries will address at a summer meeting. a) Find the number of arrangerments that can be made so that 1)A will speak before C, 2)A will speak before C and C will speak before E. b)In how many of those ways in a2) will C speak immediately...

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'm on page 31 now (of this book: http://www.math.miami.edu/~ec/book/). The question is: Show that if there is a bijection between X and Y , there is an isomorphism between S(X) and S(Y). I see the bijection btw S(X) and S(Y) in my head, but can't find the right mathematical symbols to...

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...

pizza store has small/medium/large with 10 different toppings 2 crusts and 3 types of sauses. how many ways to ordera pizza with atleast 1 topping and 1 sauce?

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.

:rolleyes: I can normally do combinations and permutations, but these two currently stump me. Any help is appreciated. :confused: 1) Twelve students are in a class. They are split so that five go to room A, four go to room B and three go to room C. How many different ways can this happen...

how do u solve for n? nP3=720...n!/(n-3)!=720...do u just start cancelling? that will be n(n-1)(n-2)=720...but its such a big number...is there another easier way to do it?

Permutations... How do u find the number of paths in a 3D object?...let say a cube...from A to B...

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!

Question Let S_n be the symmetric group on n letters. (i) Show that if \sigma = (x_1,\dots,x_k) is a cycle and \phi \in S_n then \phi\sigma\phi^{-1} = (\phi(x_1),\dots,\phi(x_k)) (ii) Show that the congujacy class of a permutation \sigma \in S_n consists of all permutations in S_n...

Hi, Is there a general method, given \sigma and \rho in Sn, for finding a permutation \tau in Sn such that \rho = \tau ^{-1} \sigma \tau? I know how to do it when \sigma and \rho are made of a single k-cycle, but what happens when they are more complex? For example, for: \sigma = (1...

Was just wondering if there was a "shorter" method of solving this problem. nPr = 60. nPr = n!/(n-r)! n=? r=3 Works out to be n(n-1)(n-2) = 60. From here on, what different options do I have? I have several ways of solving it, but was wondering what would be the "easiest"...

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...

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...

ok, very very simple, but I cannot for the life of me remember this. why is (12)(13) = 132? I can't work it out...

8 permutations that commute... Find 8 Permutations that commute with alpha=(1,2,4,5) I do not understand the concept of commuting with permutations.

Can someone help me? I need to prove that for m>=2, m permutations can be written as at most m-1 transpositions. I can't figure this out for the life of me! thanks in advance :confused:

1) In S6 find 12 permutations that commute with alpha=(1,2,4,5) i did (5,1,2,4) (4,5,1,2) (2,4,5,1) ?i don't know if transposition answers this? but i also did (1,5)(1,4)(1,2) and similar for the ones above i also used (1,2,4,5)(2,1) (1,2,4,5)(4,5)...

Hi guys, I'm new in this forum, so i hope you can help me with these problems. It might be easy, but i just started taking Elementary stats... so here they are... a) how many possible arrangements are there of the six letters {a,b,c,d,e,f} in which b and c are next to each other? b) how...

I have been working with the following question for quite awhile: Show that a permutation with an odd order must be an even permutation. I have made some progress, but I am having trouble putting it altogether to make my proof coherent. This is what i have so far...

I missed the day when my teacher went over Permutations. If someone could help me with the questions below, that would be great. What are the Permutations of the word "Saskatchewan"? 10 PrN(right?) 6 = The amount of different ways 10 units can be organized into 6 units? 6! = 6 x 5, 6 x...

I am trying to read through and understand about permutations, and I have a couple of questions. First, How do you write a permutation as a transposition? The example that I have is (3, 10, 1, 4, 5, 7, 2, 8, 6, 9), and I said that it is equal to (3, 10)(10, 1)(1, 4)(4, 5)(5, 7)(7, 2)(2...

Say I have 5 computers. How many permutations are available?

How many permutations of the letters a, b, c, d, e, f, g have either two or three letters between a and b? My guess for this is that if a and b have to have two letters between them, then there are 5! ways to arrange the rest of the letters, right? Same deal if a and b have to have three...

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 can I solve these two problems? P(n,3)=210 and P(5,r)=20 For the first one I got up to n(n-1)(n-2)=210 but I don't know how to solve a cubic equation...And the second one I have no clue. I'd appreciate some help, thanks

Hello, I am a little confused about an example. By definition, A cycle of m symbols CAN be written as a product of m - 1 transpositions. (x1 x2 x3 ... xn) = (x1 x2)(x1 x3)...(x1 xn) Now Express the permutation (23) on S = {1,2,3,4,5} as a product of transpositions. (23) =...

I need help with these two questions: How many permutations are there of the word collect if the 2 l's have to be together and the two c's have to be separated? I got as far as 360 because if u keep the l's together you would get 6! x 2! 2! x 2! but after that I am stuck on what to do...

Hello, I am having trouble understanding permutations. Here is the definition that I was given: Let A be a nonempty set, A permutation of A is any function [alpha]: A --> A such that [alpha] is both one-to-one and onto. Then the example: Let A = {1,2}. Then the permutations of A are...