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

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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: ...
2
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4answers
308 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 ...
2
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0answers
32 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
14 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 ...
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1answer
38 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 ...
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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 ...
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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 ...
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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 ...
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0answers
30 views

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 ...
2
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1answer
19 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): ...
3
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5answers
75 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
25 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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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 ...
3
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2answers
89 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 ...
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1answer
21 views

Permutation conjugate [on hold]

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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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
37 views

Find the number of ways [on hold]

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 ...
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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 == ...
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0answers
17 views

Circular Permutation with restriction [on hold]

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.
0
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3answers
60 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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2answers
49 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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0answers
36 views

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

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 ...
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 ...
1
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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
26 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. ...
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
24 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
54 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 ...
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0answers
42 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
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
31 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 ...
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3answers
36 views

No. of different possible arrangements.

How can I find no. of different possible arrangements with the factor of the term $a^2b^4c^5$ written at full length.
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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?
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3answers
19 views

Showing product of disjoint cycle

I am trying to show the product of two disjoint cycles such that they have nothing in common for $A_n$ for $n\ge 3$. So I have the two cycles $(ab)(cd)$. I have read here: ...
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3answers
36 views

Probability question - arranging 20 pupils in a row - 8 boys and 12 girls

We have 20 pupils in class, 12 girls and 8 boys. We arrange the pupils in a row, and now need to calculate the following probability: a. The probability that Jana, one of the girls, will not stand ...
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0answers
56 views

Approach name - Ross Millikan's answer

I want to know the name of an approach (formula) in the first comment of this question (@Ross Millikan's answer) Counting arrays with gcd 1 Thanks
2
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1answer
96 views

Select k no.s from 1 to N with replacement to have a set with at least one co-prime pair

Given $1$ to $N$ numbers. You have to make array of $k$ no.s using those no.s, where repetition of same no. is also allowed, such that at least one pair in that chosen array is co-prime. Find no. of ...
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2answers
46 views

Permutation order

How do you put non disjoint permutation cycles into disjoint cycle form? For Example the permutation in non disjoint cycle form (1352)(34)? How do you form disjoint cycle for from this?
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0answers
133 views
+100

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 ...
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3answers
27 views

Grandfather-Grandchildren Family Photograph Combinatorics Problem.

In how many different ways a grandfather along with two of his grandsons and four granddaughters can be seated in a line for a photograph so that he is always in the middle and the two grandsons are ...
0
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1answer
10 views

If I'm counting the number of binary strings of a certain length with a certain number of 1's, should I use combinations or permutations?

And should I use repetition allowed, or repetition not allowed formula? A binary string is a string with 1's and 0's in a row. {0,1} is a different string from {1,0}. Say I'm considering binary ...
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5answers
245 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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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 ...
2
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1answer
26 views

How many ways are there to arrange k out of n elements in a circle with repetition?

If you a set of the n elements, in how many ways $Q(n,k)$ can you take some of them and arrange them on a $k$-gon, when repetition of one element is allowed but rotations of one arrangement are not ...
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0answers
14 views

Distance between element and its position in permutation

Consider a permutation $\pi$ that is chosen uniformly at random among all permutations of $\{1, \dotsc, n \}$. Let $a_i$ be the position of $i$. We want to find $$E[\sum_{i=1}^n |a_i -i |]= ...
2
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0answers
20 views

Need a hint with permutations and pigeonhole-principle question

let $\pi_1,\pi_2,\pi_3\in S_{28}$. Help me prove that there are two sub-sequences of 28 with length 4 $i_1< i_2 <i_3<i_4,\ and\ \ j_1<j_2<j_3<j_4$ so that $\pi_q(i_n)=\pi_p(j_n)$ ...
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1answer
34 views

Primitive Permutation Group and Centralizers

Automorphism group of the Alternating Group - a proof In the above question, Derek Holt asserts that a primitive permutation groups has trivial centraliser in the symmetric group. Since I could not ...
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3answers
30 views

A test contains 10 T/F questions, 5 must be marked true, and 5 false…

A quiz consists of ten true/false questions. a) In how many distinct ways can the quiz be completed if no answers are left blank? b) In how many ways can the quiz be completed if five questions must ...