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

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$\langle g\rangle$ is $p$-Sylow subgroup of $G_\Delta$?

Let $p$ be a prime and $G$ a primitive group of degree $n=p+k$ with $k\geq3$. If $G$ contains an element of degree and order $p$. $G$ contains the cycle $(1,2 ... p)=g$. Let $\Delta= \lbrace ...
1
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2answers
87 views

Permutation of positive real numbers

Consider a set of positive real numbers $\{P_1,P_2,\dots,P_n\}$ and a permutation of this set $\{Q_1,Q_2,\dots,Q_n\}$. Is it possible to find a permutation such that ...
6
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0answers
35 views
+50

Product of permutations of consecutive numbers yields arithmetic sequence

Let $n\geq 3$ be an integer, and $a,b$ be positive integers. Let $c_1,\ldots,c_n$ be a permutation of $a,a+1,\ldots,a+(n-1)$, and $d_1,\ldots,d_n$ be a permutation of $b,b+1,\ldots,b+(n-1)$. Is it ...
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2answers
26 views

Permutation/Combination question on dice

Question: Three dice (six faces: each face -> number 1 to 6) are rolled. What is the number of possible outcomes such that at least one die shows number 2? My attempt: One die has to show two. ...
5
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2answers
41 views

Distributing candies

Suppose ther are B boys and G girls in a classroom.Teacher wants to distribute candies among B boys and G girls such that: 1.Each student gets atleast one candy and atmost N candies. 2.sum of ...
2
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4answers
66 views

How to find the number of possible outcomes of 10 games between 20 teams?

Hi I am looking for an equation to find possible combinations in a non repeating format with a twist. Here is the example: There are 10 games between 20 teams. I have to chose 5 winners but ...
0
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1answer
33 views

Number combinations - website [on hold]

There are four directions: up, down, left, right. (I am programming something). Four patterns with one (up, down, left, right), 16 patterns with two (up up, up down, up left, up right) and so on. I ...
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0answers
22 views

Permutations and combinations - fun questions [on hold]

Well I am studying permutations and combinations, and I'm finding it quite an interesting topic. Surprisingly enough, it seems to have practical applications. I was looking for some questions on the ...
4
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4answers
527 views

Is it possible to permute an unknown binary sequence so that two particular bits are equal?

A blind mathematician is give a $2015$ bit sequence. The mathematician can take any two bits and switch them (so the bit in position $A$ goes to position $B$ and vice-versa). He knows at what position ...
3
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2answers
93 views

Christmas protocol

Since holiday season is coming, here is a little practical-purpose combinatorics question. Lots of group of friends or families practice the random variant of Secret Santa, where each member buys a ...
0
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0answers
15 views

How to count arrangement of ranked criteria uniquely? (permutation problem)

My question is rather simple, but i cannot find a formula for it, here it is: 1) Suppose i have a set of criteria, which i need to rank in order of importance: 0 = most important, 3= least -height: ...
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0answers
38 views

Distinguishable balls in distinguishable boxes?

Suppose I have $n$ distinguishable balls and $N$ distinguishable boxes. A particular configuration of this 'system' is such that there are $k$ particles in a box, b, where $1\lt b \lt N$ (i.e. the ...
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1answer
16 views

isoperimetric inequalities in permutohedron

Consider the graph whose vertices are all n! permutations of numbers 1..n and there is an edge between two vertices iff we can get from one to another by an adjacent transposition. We call this graph ...
0
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1answer
42 views

Representing group by permutaions

Let the group is given by this relations $<a,b\ |\ a^5=b^4=e,bab^{-1}=a^2>$. I am asked to find the cycle index of this group. In order to find cycle index I need to represent the group with ...
1
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1answer
33 views

Is it a Permutation or Combinatorics?

I'm a programmer and I need to write an algebraic notation for a LOOP made in one of our programs. I don't have Mathematica software, but just MathType to write formulas and notations. The program ...
0
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1answer
17 views

Finding nth permutation in dictionary order with repeats

Given a set of symbols (e.g. $(A, A, B, B, B, C, D, D)$), calculate the nth permutation sorted in alphabetical order. I know how to do this with a set of symbols containing no repeats, but I can't ...
3
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1answer
13k views

How many possible combinations in 8 character password?

I need to calculate the possible combinations for 8 characters password. The password must contain at least one of the following: (lower case letters, upper case letters, digits, punctuations, special ...
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0answers
43 views

Other Patterns in Triples

I have the following 20 triples generated by polynomial distribution: $$\begin{matrix} (2,4,5)&(2,3,4)&(2,3,5)&(1,4,5)&(2,2,4)\\ ...
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2answers
24 views

combinations of 10 objects - of which 3 are distinct [on hold]

I need to count all possible combinations of a, b and c. There are 10 positions. Possible arrangements are: aaaaaaaaaa or aaaaaaaabb or aaaaaabbcc Permutations doesn't count twice: aaaaabbbbb == ...
5
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0answers
183 views

Factorizations in the symmetric group

Notation notes: The cycle $(i,i+1,\dots,j)\in S_n$ is the permutation $(1)(2)...(i,i+1,\dots,j)\dots(n)$ in cycle notation. Motivation Given a factorization of a permutation into certain cycles ...
0
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1answer
15 views

No. of ways to shuffle a card

How many ways are there to shuffle N cards such that exactly one card is in the same position?(Assuming that initially the card no. 1 is in the first position,card no.2 is in the second position and ...
2
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1answer
21 views

Every solution of a permutation equation?

I have the three permutations $$a=(1\;3\;4\;8),\quad b=(2\;3\;5\;7),\quad c=(4\;3\;2\;8)$$ and I have to find all $x$ satisfying $$axb=c.$$ I have found one solution (I hope it's good): ...
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5answers
76 views

There are $n$ persons sitting around a table…

There are $n$ persons sitting around a circular table. Then, in how many different ways 3 persons can be selected if none of them are neighbours. My approach:- Let us pretend that we have already ...
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3answers
27 views

Finding number of integral solutions

I am really getting confused in this question. Number of integral solutions of the equation. $x_1x_2x_3x_4=770$ options- $2^{11}$ $2^{10}$ $4^4$ $5^5$ I attemtemted it by saying that ...
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2answers
66 views

Combinatorics in a Party.

There are 12 persons in a dinner party, they are to be arranged on two sides of a rectangular table. Supposing that the master and the mistress of the house have are always facing each other, and ...
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2answers
573 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 ...
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2answers
50 views

Forming a committee

Suppose a committee must be formed from a group of 15 professors and 10 administrators. How many committees can be formed if the committee must consist of 5 professors and 5 administrators? Update 1: ...
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3answers
60 views

Why is this combinatoric solution not correct?

I'm trying to solve the following problem: Balls of the colors red, orange, yellow, green, blue, indigo, violet (7 colors, 1 ball per color) are placed into 4 different boxes A,B,C,D so that no box ...
4
votes
1answer
416 views

Permutations of a set with a conditional subset

Using the digits 1, 2, 3, 5, 6, 8, 0 only once, how many 4-digit numbers could be constructed if the number is even? This is an exercise from an online course I'm taking. The given solution suggests ...
1
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1answer
21 views

Permutation conjugate [closed]

I have to conjugate $a$ with a permutation, to get $b$. $$xax^{-1}=b$$ What is $x$, if $a = (1,3,4,8)$ and $b = (2,4,5,7)$? And how to solve it?
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5answers
250 views

Permute “aaaaabbbbbccccc” so that no two identical letters are adjacent

This is a follow up question to Application of PIE. How many strings with the letters "aaaaabbbbbccccc" are there so that no two identical letters are adjacent?
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3answers
65 views

Probability of Permutations/Combinations

How do you set up the formula for the probability of a permutation/combination? Question: If you have a group of candy with $2$ Snickers, $4$ Kit Kats, and $2$ Butterfingers and you take two pieces ...
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2answers
37 views

Find the number of ways [closed]

If there are 5 speakers A,B,C,D and E.The number of ways in which A will speak alwways before B would be? There are the options given a.24 b.4!*2! c.5! d.none can anyone mention the right option ...
0
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0answers
20 views

Circular Permutation with restriction [closed]

3 ladies and 3 gents can be seated at a around table so that any two and only two of the ladies sit together.The number of ways is a.70 b.27 c.72 d.none please mention the answer with process.
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3answers
61 views

Why is this $6!$ factorial and not $p(6,1)$?

There is this question. There are six different candidates for governor of a state. In how many different orders can the names if the candidates be printed on a ballot? The answer is $6!=720$. But ...
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0answers
36 views

Great wisdom is need here…can YOU help? [closed]

a referendum is conducted with twenty five people given the chance to vote yes or no. each ballot box must contain at least 8 votes each how many possible outcomes are there? order of picks do not ...
0
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3answers
384 views

Counting arrays with gcd 1

I want to calculate the number of arrays of size $N$, such that for each of it's element $A_i, 1 \leq A_i \leq M$ holds, and gcd of elements of array is 1. Constraints: $1 \leq A_i \leq M$ and $A_i$ ...
2
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1answer
39 views

There are 10 stations on a circular path

There are 10 stations on a circular path. A train has to stop at 4 stations such that no two stations are adjacent. How many such selections are there?? Since i know if the stations are on the ...
0
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1answer
55 views

Combinations. x+y+z=12 [closed]

X+y+z=12 x,y,z are all greater or or equal to 0 and are integers No. of combinations of x,y,z are ............. *note-- (12,0,0) and (0,12,0) are treated as same Please solve this by using formulae ...
4
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4answers
408 views

Is it always true that (a,b,c)(a,b,c) = (a,c,b)?

I notices that $(1,2,3)(1,2,3) = (1,3,2)$ and i also noticed that $(1,4,3)(1,4,3) = (1,3,4)$ and so is it true that for any permutation $(a,b,c)^2 = (a,c,b)$
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1answer
28 views

Simplifying Permutations

Could someone explain the process of simplifying the following permutation in $S_6$ (1,3,5)(2,4,5)(2,3,6) An explanation on how you arrived at the simplified form would also be greatly appreciated. ...
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2answers
27 views

How many ways are there to place 7 distinct balls into 3 distinct boxes?

How many ways are there to place $7$ distinct balls into $3$ distinct boxes? is the question I'm confused about. The solution shows that the correct answer is $3^7$. I'm just confused why this is. ...
1
vote
1answer
25 views

Number of permutations of m objects taken out of n objects where an object can repeat any number of times.

I'm given $n$ distinct objects. In how many ways can we select and permute $m$ objects out of those $n$ objects. $n$ may be less than $m$ and any object can appear any number of times. For example: ...
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2answers
20 views

License plate permutations [closed]

If a license plate is to have 3 letters followed by 3 digits and repetition of letters and digits is allowed how many different license plates can be made?
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1answer
38 views

How many ways can we place two types of balls on a circle?

There are $a$ red balls and $b$ blue balls, and I have to place all of these balls on circumference of a circle. The balls with the same color are indistinguishable. I thought the answer would be ...
1
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2answers
37 views

In how many ways can I merge $m$ and $n$ items without disturbing the order in each group?

I have two lists having all distinct elements. One contains $m$ elements and other contains $n$ elements. We need to arrange them such that the order of elements of individual lists is not disturbed. ...
1
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1answer
32 views

How many ways are possible to place k items in n spots such that order of k items is not disturbed

I have k items, need to place them in n spots(n>k). In how many ways can this be done? Example - for k=2 and n=4, these are the possibilities assuming items to be like this [1,2] 12-- 1-2- 1--2 -12- ...
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0answers
19 views

What is the algebra behind the Cuthill Mckee Bandwidth Reduction

From my understanding a Sparse matrix is converted to banded matrix and then the cuthill mckee is used to reduce the bandwidth. I have spent about three days browsing the web to find an example where ...
3
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1answer
42 views

Let there be 9 fixed point on the circumference of a circle.

Let there be 9 fixed points on the circumference of a circle. Each of these points is joined to every one of the remaining 8 points by a straight line and the points are positioned on the ...
5
votes
3answers
54 views

if $m, n \in \mathbb{N}$, $m < n$, then $S_m$ isomorphic to subgroup of $S_n$

How do show that if $m, n \in \mathbb{N}$ and $m < n$, then $S_m$ is isomorphic to a subgroup of $S_n$, without using any "overpowered" results?