For questions related to permutations, which can be viewed as re-ordering a collection of objects.

learn more… | top users | synonyms

2
votes
2answers
104 views

Is there a solution to this Seating Plan problem?

So a colleague asked me for some Help on an interesting Problem, which we both couldn't find the optimal answer for. The event which needed it is already in the past, so this is just me trying to ...
1
vote
1answer
97 views

How many ways to paint a board with 2 colors..

You got a fence, you need to paint the boards with black and white, but can not have 3 or more boards same color in a row. how many ways do you have?
1
vote
1answer
47 views

Using that $G$ is isometric to a subgroup of $S_G$ to prove something about $G$

I am doing the following exercise for an assignment: Assume that $G$ is any finite group with non-trivial elements such that $bab^{-1}=a^{-1}$. Let $k$ be a natural number and use induction to ...
0
votes
2answers
29 views

Permutation and combinatorics problem

How many numbers between 10 and 1000 can be formed using digits 3,4,5,7? Should we first find number of 2 digit numbers and then find number of three digit numbers and add them
0
votes
2answers
22 views

every k cyclic is a product of at least k-1 distinct tranpositions

There is a theorem says if $A$ in $S_n$ is a $k$ cycle, and $A = a_1 a_2 a_3 \dots a_m$, where $a_i$ are transpositions, then $m \geq k-1$. But how to show there are at least $k-1$ distinct ...
2
votes
3answers
176 views

In how many ways can the couples sit?

$4$ married couples are to be seated on a circular table with $8$ identical seats. In how many ways can they be seated so that (i) males and females sit alternately and (ii) no husband sits adjacent ...
3
votes
3answers
314 views

How many different 4 digit combinations will include at least one 7, assuming numbers cannot repeat

I cannot get the correct answer - $2016$. What I have tried so far is thus: the number $7$ can occur $1, 2, 3,$ or $4$ times. Since it is a combination we do not care if the number starts with zero ...
3
votes
3answers
243 views

What does “order matters” regarding permutations refer to?

I psychoanalyze EVERYTHING and permutations/combinations are frustrating me. Sorry for posting so many questions lately but I really appreciate all of the help! Ok so I know the permutation formula: ...
0
votes
1answer
43 views

Can someone please explain the reasoning for this permutation problem?

I'm studying and reading through my discrete math book.. I seemed to be grasping the idea of permutations, but I don't understand how the solution for this particular problem came to be. Question: ...
1
vote
0answers
29 views

Arrangements of numbers when each can have multiple values?

I feel as though this is fairly straightforward, but I can't figure it out. If I have $n$ numbers, clearly these can be arranged in $n!$ ways. But if each of the $n$ numbers can have a value $v, ...
0
votes
2answers
125 views

Permutations of a letter sequence

I have been given a question about (i think) permutations, it asks to find how many x letter sequences can be made out of a word. I am getting confused because it first asks how many different ...
0
votes
3answers
43 views

Generate a power set by only adding or removing a single element at a time

Is there an algorithm that is capable of generating a complete power set by only removing or adding one element in each step? I'd like it to avoid duplicates, but ordering isn't important. I've tried ...
0
votes
2answers
50 views

How many skew symmetric matrices are possible?

I just heard the term skew symmetric matrix and upon discovering what it was, I thought to myself, "Jeez, there could only be so many of those." I'm not good with the whole permutation thing and this ...
1
vote
1answer
53 views

What mathematical algebra explains sequence of circular shifts on rows and columns of a matrix?

Consider a simple matrix (3X3) with entries thus: [1 2 3; 4 5 6; 7 8 9;] Circular shifts can be performed on any row or any column thus: row-(1/2/3)-(right/left) and column-(1/2/3)-(up/dn) ...
2
votes
2answers
95 views

Find the center of the symmetry group Sn.

Find the center of the symmetry group $S_n$. Attempt: By definition, the center is $Z(S_n) = \{ a \in S_n : ag = ga \forall\ g \in S_n\}$. Then we know the identity $e$ is in $S_n$ since there is ...
0
votes
1answer
70 views

How to show that a permutation form a group?

Given the following $12$ permutations: $\{(1), (123), (132), (124), (142), (134), (143), (234), (243), (12)(34), (13)(24), (14)(32)\}$ (a) Show that the 12 permutations form a group. (b) Find ...
3
votes
1answer
70 views

Can someone please clarify combinations vs permutations?

I see similar questions asked on here and obviously I did some research and read my book, but it seems like every explanation contradicts another in some way. There are basically infinite scenarios ...
0
votes
1answer
33 views

Permuation & combination on finding number of ways lid can be wrongly placed

There are 5 bottles of sherry and each have their respective caps. If you are asked to put the correct cap to the correct bottle then how many ways are there so that not a single cap is on the ...
0
votes
1answer
33 views

What number of robbers, under the model of the prisoner's dilemma, would be optimal?

The prisoner's dilemma is defined as "Two members of a criminal gang are arrested and imprisoned. Each prisoner is in solitary confinement with no means of speaking to or exchanging messages with ...
1
vote
5answers
523 views

Probability [Sum of digits is even for a random number] [closed]

A number of 6 digit numbers is written down at random. Probability that the sum of the digits is an even number is? Please answer with explanation.
1
vote
2answers
124 views

Probability [Distinct balls in distinct boxes]

6 different balls are put in 3 different boxes, no box being empty. The probability of putting balls in the boxes in equal numbers is ? Could anyone pleases give the answer and explain it.
1
vote
1answer
42 views

Seating Plan for meetings

I really don't know how to describe this but appreciate any help in solving it: We hold a weekly meeting with a variable number of attendees (Currently between 20 & 24) and currently arrange them ...
0
votes
1answer
138 views

How many natural numbers not more than 4300 can be formed with the digits 0,1,2,3,4 (if repetitions are not allowed)?

My Approach: Total no of available digits: 5 No of 1-digit formed: 5 No of 2-digit formed: 4(excluding '0' on ten's place) * 4 (including zero - one among given digits already used) No of 3-digit ...
0
votes
1answer
51 views

Just double checking if I am doing this correctly.

A professor writes 40 discrete mathematics multiple choice questions each with three possible answers, a), b), or c). If there are absolutely no constraints on how many questions can have answer a) or ...
2
votes
0answers
18 views

Clarification on a cycle parity proof

Prove that cycle $(a_1a_2...a_k)$ is even $\iff$ $k$ is odd. This makes intuitive sense because $(a_1a_2a_3...a_k)=(a_1a_k)(a_1a_{k-1})...(a_1a_3)(a_1a_2)$ which will be an even number of ...
0
votes
2answers
22 views

Dividing $N$ into $n$ groups such that a specific pair is a member of at least one group.

$N$ is a set, $\{a_1,a_2,a_3,...,a_r,x,y\}$ and has to be divided into $n$ groups, such that one of the groups has both $x$ and $y$. How do I find the number of ways to do this?
1
vote
2answers
57 views

what is degree of permutation group?

Is "degree" the same term as "order" of a permutation group?
0
votes
2answers
38 views

permutation cycle group of a large power

I was going to add this to my previous question here, but I didn't think that was allowed. The question I have here: (1254)^1000 How would I find something of this large? Would I be able to do ...
0
votes
1answer
56 views

Permutation cycle notation

I'm trying to compute (12)(1253) What I Did: I started with 1, and 1 goes to 2 and 2 goes to one, so (12). Then I did 5, which goes to 3. 3 goes to 1 and 1 goes to 2. Then 2 goes to 5, so it's ...
0
votes
1answer
37 views

Conjugate cycles

Prove the following in $S_n$: Let $\alpha = (a_1,a_2,\ldots,a_s)$ be a cycle and let $\pi$ be a permutation in $S_n$. Then $\pi\alpha\pi^{-1}$ is the cycle $(\pi(a_1),\ldots,\pi(a_s)).$ I'm not ...
2
votes
1answer
54 views

Mary can answer 20/25 problems correct… simple probability

Question: A teacher gave his class $25$ problems and told his students that he would select $10$ of them to put on their midterm. Mary can figure out how to answer $20$ of the problems, what is the ...
0
votes
1answer
40 views

What's the difference between a permutation and a combination with repetition?

My understanding is that a permutation is used to find the number of rearrangements of different elements, taking into account possible orders. A combination is used to find the number of ...
2
votes
0answers
41 views

Multiple Hypergeometric Distributions

I need to figure out a problem which involves multiple hypergeometric distributions. Referring to the Urn problem, the problem can be described like the following: We have $n$ urns $u_1,…,u_n$. Urn ...
2
votes
1answer
58 views

Using combinatorial reasoning to show $n!=\binom{n}{0}D_n+\binom{n}{1}D_{n-1}+\dots+\binom{n}{n}D_0$

How can one use combinatorial reasoning to show that $$n!=\dbinom{n}{0}D_n+\dbinom{n}{1}D_{n-1}+\dbinom{n}{2}D_{n-2}+....+\dbinom{n}{n-1}D_1+\dbinom{n}{n}D_0$$ Now $D$ stands for deranged which is a ...
0
votes
0answers
37 views

Permutation And Combination: Finding suitable number of intial permutations of numbers 1 to N

We have first N natural numbers where N=2^k for some 1<=k<=20. The numbers are arranged in random order consecutively in a line. There are k steps. In each step greater of the two numbers at ...
1
vote
1answer
34 views

Largest Number Drawn - Why are These Approaches Not Equivalent?

Here's the question: Four numbers are drawn at random from a box of ten numbers 0, 1, ..., 9. Find the probability that the largest number drawn is a six if the draws are made with replacement. The ...
2
votes
4answers
68 views

determining the amount of total questions needed in a game given the probabilty

I'm creating a game and can't seem to quite figure this out - driving me crazy. There are 8 questions in my game You can play the game an unlimited amount of times the test bank doesn't change. so ...
0
votes
2answers
126 views

Permutation and combination problem - word arrangement

This is a question of permutation and combination. Q. How many words can be formed from the word "LUCKNOW" when i) No restriction is there ii) L is the first letter of the word iii) All the ...
5
votes
0answers
133 views

How find this $aA_{m+1}=\overline{\sigma_{0}\sigma_{1}\sigma_{2}\cdots\sigma_{m}}$

Question let $m$ is positive numbers,and such $m\ge 5$,and $$A_{m+1}=\overline{1234\cdots m}=1\times (m+1)^{m-1}+2\times (m+1)^{m-2}+\cdots+(m-1)\times (m+1)+m$$(or see ...
1
vote
1answer
78 views

In how many ways can you arrange the alphabet so that A and B are always next to one another (In either order)

Ok, so I have no idea where to begin on this question. Do I treat A and B as one letter? 25 choose n?
1
vote
1answer
56 views

How many ways are there to arrange 1's and 0's with no two 1's in a row? [duplicate]

Given n spaces, how many ways are there to fill up the spaces with 1's and 0's such that no two 1's are together. For example, let's say n = 3 (_ _ _). There are 5 ways to fill up the spaces such ...
1
vote
1answer
64 views

Calculate total number of combination of 4 characters having pattern as Letter-Number-Letter-Number

I need to know "How" to calculate total number of combinations that are possible to generate 4 character string having a pattern of Letter-Number-Letter-Number. The complexity are: strings should be ...
1
vote
1answer
19 views

What are the number of circular arrangements possible?

Suppose we have $4$ identical red beads and $3$ identical blue beads. In how many ways can we form a necklace out of these? I am a little confused here. Suppose we fix a red bead and treat the ...
2
votes
1answer
53 views

Finding $\lim\limits_{n\rightarrow \infty}\sum\limits_{r=1}^{n}\frac{1}{T_r}$ given $\sum\limits_{r=1}^{n}T_r=\frac{n(n+1)(n+2)(n+3)}{8}$

If $\displaystyle\sum_{r=1}^{n}T_r=\frac{n(n+1)(n+2)(n+3)}{8}$, then how can we find $\displaystyle\lim_{n\rightarrow \infty}\sum_{r=1}^{n}\frac{1}{T_r}$?
0
votes
0answers
31 views

Construction of transitive group of degree $n$

Is there any way to construct all transitive groups of degree 6 with the following block system: {1,2} , {3,4}, {5,6} ?
1
vote
2answers
43 views

Permutation help

Consider the elements of $S_7$. For each $\sigma \in S_7$ there is a smallest positive integer |$\sigma$| such that $\sigma^{|\sigma|}=e$. Find the value of $N$= max{ $|\sigma|$ | $\sigma \in S_n$}. ...
0
votes
1answer
32 views

Finding a permutation from a power of itself

Find a permutation $\sigma \in S_9$ such that $\sigma^2=(13579)(268).$ So I know that $\sigma^{10}=\sigma.$ But I don't know $\sigma^5$..... Is $\sigma^{10}=\sigma^4\sigma^6$? I doubt this is the ...
0
votes
1answer
257 views

How many different ice cream cones with 31 different flavors and 2 kinds of cones?

I have been trying this for a while now. Using the formula for permutations, I am getting P(31, 2) = 10,230, but this seems way too high... An ice cream shop has 31 different flavors of ice cream and ...
0
votes
2answers
63 views

If a club has 24 members, In how many ways can 4 officers be chosen from the members of the club?

I understand the concept of combinations and permutations. However, I am not getting how to apply the formulas. I believe understanding exactly how to do this would help.A club has 24 members. a. In ...
1
vote
1answer
161 views

Permutations/Combinations: How many different passwords are possible?

Hello everyone. I have a couple questions this time, but I think if I understand how to do this one, I'll understand the others. A particular online banking system uses the following rules for its ...