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

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Number of ways so that exactly one permutation of the word TIDE occurs

I want to calculate the number of $8$ letter words that can be formed using the letters of the word $TIDE$. However, in any word only one permutation of the word $TIDE$ should be present. That means ...
3
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3answers
39 views

In how many ways $A$ speaks before $B$ and $B$ speaks before $C$

$10$ persons has to give a speech among which three are $A$, $B$ and $C$. In how many ways can they give speech so that $A$ speaks before $B$ and $B$ speaks before $C$. I have taken the fixed speech ...
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0answers
33 views

If $G$ has cyclic Sylow $2$-subgroups, then the core $O(G)$ acts transitive.

Let $G$ be a finite, transitive permutation group on $\Omega$, and assume the point stabilizers have even order. Denote by $O(G)$ the largest normal subgroup of $G$ whose order is odd (see here for ...
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0answers
47 views

If $G$ acts such that $\mbox{fix}(g) \in \{0,3\}$ for $g \ne 1$, and stabilizers are t.i. subgroups, then the Sylow $3$-subgroups have maximal class

Let $G$ be a transitive permutation group such that every nontrivial element fixing some point fixes exactly $3$ points. Also assume that for $g \notin N_G(G_{\alpha})$ we have $$ G_{\alpha} \cap ...
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1answer
62 views

Extend isometry on some cube vertices to the entire cube

Let $K\subset V=\{-1,1\}^n$ be a set of vertices of the $n$-dimensional hypercube $D=[-1,+1]^n$ and let $f:K\to V$ be an isometry with respect to the Euclidean metric inherited from $\mathbb R^n.$ We ...
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3answers
56 views

Permutations and combinations textbook recommendations

I have had real difficulty with permutation/combination questions in probability and statistics texts. What I have real difficulty with is transforming word problems into mathematical form to solve. ...
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2answers
25 views

Combinatorics question- 8 football games- how many end with 4 wins, 3 losses and a tie

A college plays 8 football games during a season. In how many ways can the team end the season with 4 wins, 3 losses and a tie? I started this question by trying to count the total number of possible ...
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0answers
13 views

Qualities of Even Permutation Groups

I need some help figuring out some qualities of even permutation groups. Consider $E_n$ to be a subset of the bijection set $S_n$ (bijections over $[n]$) that consists of all even permutations. I want ...
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1answer
19 views

Proving Property of Certain Permutation Groups

I'm trying to show that there is no $g$ such that $g^{-1}(1,2,3)g = (1,3)(5,7,8).$ I am having some general issues figuring out where to move with this problem, since it seems difficult to figure out ...
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1answer
55 views

How many move paths on a 2-d grid? [duplicate]

On a 2-d grid how many different move paths can be made that begin at $(0,0)$ and end at $(x,y)$ with $x\gt 0$,$y\gt 0$. Restriction : left,down and diagonally moves aren't allowed .
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1answer
25 views

Finding the number of objects in permutation [closed]

What is n in this permutation, P(n, 3) = 60? Please help me solve this.
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1answer
41 views

Permutation problem: create words from letters

I'm stuck on this problem: Consider the five letters A, B, C, D, and E. How many words with four letters can you create if each letter can be used at most two times? (One letter can i.e. be used ...
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0answers
42 views

Fast way to multiply permutation groups?

I'm having some trouble with permutation group multiplication. When multiplying permutation groups, I always follow the method described in this post: multiplication on permutation group written in ...
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2answers
80 views

Domino tiling extended in N dimensions.

The standard domino tiling problem, is the number of ways to tile a board of size 2xn by dominos of size 2x1. The answer directly follows a recursion, the same as the Fibonacci series. If I extend ...
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0answers
75 views

Permutations of given set. [duplicate]

Given a finite set of elements $\{a,b,c,d,e,..\}$ what will be the total number of permutations if sets of two elements each cannot occur side by side (or sequentially in order or in reverse order). ...
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0answers
33 views

Number of Sitting Permutations? [duplicate]

There are N persons. You are given M numbers of pairs from these N people. Find total no of permutations to arrange these people in a line in such a way that none of the metioned pair sit together. ...
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0answers
29 views

Permutations to divide a solid

I have a 3-dimensional cuboid, with dimensions 2x2x1. I wish to divide this into smaller EQUAL sized cuboids of size 2x1x1. Then I want to extend this case for larger cuboids, assuming that equal ...
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1answer
29 views

Left hand glove and Right hand glove

There are n pairs of gloves and n men. In how many ways can each of the n men have a left hand of one pair and a right hand of another pair of gloves. I thought its a simple question of derangements ...
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3answers
90 views

Can there be a single game of Chess which includes all the possible situations that may arise during Chess?

First of all, I am sorry as there were some completely inappropriate posts posted by my account earlier. This happened because I forgot to log my account out from the computer in Net Cafe I last ...
2
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1answer
199 views

Arrange $n$ people so that some people are never together. [duplicate]

We have $n$ number of people and some pairs given. These pairs of people are never to be together. How to calculate the number of arrangements possible? e.g we have n=4 and pairs =3 and pairs are ...
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0answers
43 views

How to calculate $a_5,a_4=$

Let $a_n$ be the number of those permutation $\sigma $ on $\{1,2,3...n\}$ such that $\sigma $ is a product of exactly two disjoint cycles .Then $a_5,a_4=?$ Calculating $a_4$ :Possible cases which ...
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1answer
62 views

How many ways to line up n objects with distinct heights

Over winter break, I have been working on a few programming questions and I came across this one, which has me a bit stumped: As you ponder sneaky strategies for assisting with the great rabbit ...
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1answer
75 views

Permutations with restrcitions

I have n distinct numbers , so I will have n! permutations. Now I want to insert another number into this set , and find the total number of new permutations. But there are some restrictions. This new ...
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2answers
57 views

Total possible permutations with certain restrictions

How to solve such questions in which we are given $N$ distinct numbers i.e $1$ to $N$ and also given certain restrictions like $(x,y) , (x,z) , (z,x) , (z,a) , (b,c)$ and so on should never occur ...
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1answer
38 views

Lottery permutations

This lottery game has a ticket where you choose 5 different numbers from 1 to 75, inclusive, in the pink part of the ticket. Then you choose one number from 1 to 15 , inclusive, from the white part of ...
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0answers
29 views

count of distinct permutation of N elements when non of the given m pairs is a part of the permutation? [duplicate]

Suppose i am having a permutation of N items(from 1 to N) and M pairs,then what will be the no of different permutations under condition that any of M pairs should not come together? For ex - Suppose ...
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3answers
54 views

Permutation of the word mathematics

How many permutations are there of the letters Mathematics? (a)How many of them begin and end with letter A? (b)How many of them does not have two vowels adjacent to one another? For (a) I got ...
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2answers
58 views

Understanding Stirling no of first kind

I was reading about Stirling no of the first kind, so $ \left[ \frac{n}{k} \right] $ represent no of k cycles of n items, so in $ \left[ \frac{4}{2} \right] $ there would be 11 such combinations, of ...
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1answer
44 views

The Relation Between Kronecker's Delta and the Permutation Symbol

The Kronecker's Delta is defined as $$\delta_{ij}= \begin{cases} 1 & i=j \\ 0 & i \ne j \end{cases}$$ Also, the Permuation Symbol known as Levi Cevita's Symbol is introduced as ...
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1answer
27 views

Combinatorics: “four male-female couples and eight chairs” problem

I was trying to solve the following problem: Eight persons, consisting of four male-female couples, are to be seated in a row of eight chairs. How many seating arrangements are there in each of ...
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1answer
342 views

Permutation of n objects with restriction of adjacent pairs

Given $n$ objects with values $\{x_1,x_2,x_3,\dots,x_n\},$ and $m$ pairs $a_k = \{x_i,x_j\}$. Let $\{p_1,p_2,p_3,\dots,p_n\}$ be a permutation of objects. The question is to find number of ...
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0answers
76 views

Find number of valid permutations [duplicate]

I have to find the number of permutations of first N natural numbers such that given C conditions should be satisfied. The C conditons can be like this 1 and 2 not occurs consecutively 4 and 5 not ...
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1answer
40 views

On diagonals that commute with permutations

Given a permutation matrix $P$ what are the elements in the set of diagonal matrices $\mathcal R$ with $\pm1$ on diagonal that commute with $P$. That is for what $R\in\mathcal R$ do we have $RP=PR$?
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2answers
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In how many ways can you pick $m$ cats from $n$ cats if $2$ given cats must never be together at the $m$-group?

In how many ways can you pick $m$ cats from $n$ cats if $2$ given cats must never be together at the $m$-group? Is it $C(n,m)-C(n-2,m-2)$, $C(n-2,m)+C(n-1,m)+C(n-1,m)$ or something else?
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1answer
44 views

How often does 7 occur from number 1 to 1000?

How many times will the digit $7$ be written when listing the integers from $1$ to $1000$? Is the following method correct? For a single $7$, $($C(1,1)$ \times$C(9,1)$\times$C(9,1)$)$$\times$3! ...
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2answers
31 views

What is the intuition for permuting $n$ objects where $p$ are alike

If we have $n$ objects in which $p$ are objects are alike and rest are all different, then the number of permutations is $\frac{n!}{p!}$. Is there some intuition on how this is correct? why do we have ...
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1answer
29 views

Multisite Permutation with Repetition

Assume you have the word 'abab'. I want to find permutation of size 2 for the word without duplication. The answer is clearly $2!=2$. However, I am struggling with finding a generalize from. My ...
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2answers
165 views

Number of possible paths

On a $xy$ plane how many $2n$-move paths can be made that begin and end on $(0,0)$ but pass from $(k,n-k)$ with $0\leq k\leq n$? I can't think of a way to solve it, because every move is allowed and ...
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2answers
32 views

Is there a formula for computing the number of arrangements from a set of N elements groupped in K groups?

Eg: N=3, K=2 There will be two groups in each solution. We need to calculate the number of such possible solutions. Consider ...
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1answer
50 views

Number of paths on xy plane

How many paths do we have that they start from $(0,0)$ pass firstly from $(3,2)$ then from $(4,5)$ and end up on $(x,y)$ if we can only go up and right. Is it right to say that the number of path are ...
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4answers
420 views

confusion about permutation

$7$ white identical balls and $3$ black identical balls are randomly placed in a row. The probability that no two black balls are together is ? I am getting it as $ \frac{1}{3}$ while the answer in ...
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2answers
38 views

To find order of permutation

Let $\sigma$ be the permutation given by Is their a short way to do this.Thanks
0
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1answer
29 views

Projective space and its basis

I am trying to solve an exercise from the book "Permutation Groups" by J. Dixon and B. Mortimer. Later, I asked a similar question about the basis of Affine geometry " Affine geometry and its ...
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1answer
45 views

Klein $4$-group

Let $G$ be a permutation group on $X$ and let $\overline{X} = X\cup {a}$, where $a\notin X$. A transitive permutation group $\overline{G}$ on $\overline{X} $ is a transitive extension of $G$ if $G\le ...
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0answers
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About a transitive permutation group of prime degree

This is not a homework! I am trying to solve the following exercise of the book "Permutation Groups" by Dixon and Mortimer: I know that $p \mid \vert G\vert$, because $G$ is transitive of degree ...
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1answer
37 views

possible number of PAN card numbers

Permanent Account Number (PAN) is a code that acts as identification of Indians. An example number would be in the form of AAAPL1234C. The format is The first three letters are sequence of ...
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1answer
34 views

How many different telephone numbers are there if it is assumed that each number contains not more than seven digits?

How many different telephone numbers are there if it is assumed that each number contains not more than seven digits (a telephone number may begin with a zero)? I am a learning mathematics as a ...
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2answers
46 views

please explain the following permutation and combination question only using concept of permutation [closed]

`In how many ways can a lawn tennis mixed double be made up from seven married couples if no husband and wife play in same set.
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23 views

Group Action and centraliser

Let Sn be the group of permutations of {1,...,n}, and suppose n is even, n > 4. Let g = (12) āˆˆ Sn, and h = (12)(34)... (nāˆ’1 n)āˆˆ Sn. (i) Compute the centraliser of g, and the orders of the ...
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2answers
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In how many ways can $7$ people be chosen out of $12$ people so that $2$ given people can never be selected together?

Is it right to take the combination of $7$ out of $12$ and subtract the combination of $5$ out of $10$ so i take out the ways that both of them are chosen? So it will be $792-252=540$ I just find ...