Tagged Questions

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

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A Proof Question

Prove : Summation(k * p(n,k)) = n! over k=1 to n, where p(n,k) is the number of permutations of {1,2, .. n} which have exactly k fixed points. I was using p(n,k) = n!/(n-p)! and trying to solve ...
2
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4answers
118 views

Problem on selecting group of card from a well shuffled pack of card

I have a problem I'm working on: The minimum number of cards to be dealt from an arbitrarily shuffled deck of 52 card to guarantee that three cards are from some same suit is which amount? I got ...
2
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1answer
30 views

Show that the permutation [n, n-1,…, 2,1] has n(n-1) inversions

Show that the permutation $[n, n-1,..., 2,1]$ has $n(n-1)$ inversions How do I show that this is true? Why isn't $(n(n-1))/2$
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2answers
21 views

Find the number of 3 letter words that can be formed from the word 'SERIES'.

To find the number of three letter words that can be formed from the word 'SERIES', with or without meaning and without repetition. The number of permutations if all letters were distinct = ...
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1answer
29 views

Permutation of $n$ women and $m$ men, in a line, where the women dont get along with each other

So the $n$ women can't sit next to each other. So in a straight line how many ways can they be seated? I know this problem is partitioning distinct balls in $n+1$ partitions, out of which $n-1$ of ...
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5answers
697 views

Even Number cards?

There are $15$ cards on a table, marked with an integer $1$ from to $15$ . How many ways can I take cards such that the sum of the numbers on the cards is even? Please help me?
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1answer
27 views

how to calculate these intersections without having to count all combinations

We have the following sets: $X= {(a,b,c,d) ∈S: b< c < d},$ $Y= {(a,b,c,d) ∈S: a< c < d},$ $Z= {(a,b,c,d) ∈S: a< b < d},$ $F= {(a,b,c,d) ∈S: a< b < c},$ Where each of ...
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0answers
12 views

Amount of inversions in permutations.

Let $I_n(k)$ be the number of permutations of $n$ values that have exactly $k$ inversions. The true is expression: $$I_n(k) = I_n\left( \binom n 2 - k\right) $$ but I don't understand why. Please help ...
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0answers
163 views
+100

Math puzzle: 10 digit strings generations

There was a question in a math competition that I attended last year. At the end of competition, I realized that my answer was wrong for the question below and I have never been able to figure out how ...
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1answer
29 views

Number of ways of choosing identical balls

Suppose we are given a bag of $n$ identical red balls, what is the number of ways of choosing $3$ red balls from the bag? I know the answer is $$ \binom n3 $$ but isn't there just one way of choosing ...
3
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1answer
29 views

Number of $k$-cycles in $S_n$

I've computed that the number of $k$-cycles in $S_n$ is $\frac{n!}{(n-k)!k}$ and wiki seems to agree with me. Now, we know that in $S_n$ the number of $k$-cycles is also equal to the cardinality of ...
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4answers
57 views

A question on colouring cubes

We are given 6 distinct colours and a cube.We have to colour each face with one of the six colours and two faces with a common edge must be coloured with different colours.How many distinct ...
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2answers
20 views

Permutations/Integer Solutions to Equations

I'm pretty lost on this so I'd appreciate some feedback as to whether or not I'm on the right track. Find the number of integer solutions of $x_1 + x_2 + x_3 = 15$ subject to the conditions $0 \le ...
0
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2answers
15 views

How can it be proven that a cycle of length k is an even permutation if and only if k is odd?

How can it be proven that a cycle of length k is an even permutation if and only if k is odd? I know it can be done using the fact that a permutation which exchanges two elements but leaves the rest ...
0
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1answer
22 views

question relate to repetition, permutation [on hold]

1) a) show that $2^n = \sum_{r=0}^n {n \choose r}$ b) in how many ways can 8 boys be devided into two unequal sets? my solution: 8P2 =56 2) to win a prize in a 'scratchit' game te ticket must show ...
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1answer
11 views

repetition of permutations problems bingo

for a game bingo, organizers place one marble with 0 marble on it, one marble with 1, and one marble with 2 and so on up to one marble with 9. Each time a number is called one number is drawn, the ...
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1answer
13 views

permutation, arrangement with restrictions, playing with vowels

in how many ways can the letters of the word "together" be arranged? In how many of these arrangements are all the vowels together? i solver the first one: (8P8)/(2P2 *2P2) =10080 but not sure with ...
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1answer
38 views

permutation (retrictions on arrangements) numbers

a list of questions :D 1) how many four digit numbers are divisible by 5 if no two digits are the same? My solution: 9*8*7*2=1008 2)From the digits 0,1,3,5,7,9 how many four digit numbers ...
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0answers
7 views

Restrictions on arrangement permutation about area [closed]

If the components of the stockyard must be used to make an outer yard 24m x 16m but the dividing fence need not be in the middle, discuss alternative yard layouts and how many arrangements of ...
0
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2answers
31 views

A tricky problem on permutation and combination

Let $A_n$ denote the number of all $n$-digit positive integers formed by the digits $0,1$ or both such that no consecutive digits in them are $0$. Let $B_n$ the number of such $n$-digits integers ...
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2answers
29 views

Dividing students into teams-combinatorics

In how many ways can $n$ number of students be divided into two teams such that each team has at least one student. This is what I did: Let $x_1$ be the number of students in the one team and $x_2$ ...
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1answer
21 views

Conjugate permutation and “their” $\alpha$

Let $\sigma=(13624)(587)(9)$,$\tau =(15862)(394)(7)$. Determine such $\alpha$ that $\alpha \sigma \alpha^{-1} = \tau $. The elements $\sigma, \tau $ must be conjugate. But how many such $\alpha$ are ...
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0answers
8 views

Composition permutation of different cycle index

What can we say about the circle index of permutations resulting from the composition of two permutations of a different circle index?
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0answers
25 views

Average number of cycles in a uniformly selected random permutation of {1,…,n} [duplicate]

I (think) I'm on the right heading with this problem, but I feel like I'm taking a jump with my reasoning and relying on intuition. I've proved combinatorially that for a permutation of $\{1,...,n\}$ ...
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2answers
61 views

How to evaluate factorials greater than $69!$

How to evaluate factorials greater than $69!$? On my calculator, $69!$ is the largest number I can enter before it gives me a syntax error, most likely due to an overflow. Is there a way to evaluate ...
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0answers
15 views

Composition of permutations different types

What can we say about the type of permutations resulting from the composition of two permutations of a different type? Is the type of permutation must be the same as the type of reversed permutation? ...
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1answer
22 views

Prove that K is subgroup.

Let K be the set of all permutations of $ S_4 $ type $ [2 ^ 2] $ and the identity permutation $\in K $. Prove that $ K $ is a subgroup $ S_4 $. I would like to prove that for$\pi, p \in S_4$ and type ...
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0answers
13 views

Logarithm of an applied permutation

Say I have a cyclic permutation $P$, a known input $x$, and a known output $y$ such that $$y = P^a x$$ for some $a$. Is there a good way to search for $a$ (i.e. better than brute force)? Are some ...
0
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0answers
40 views

Permutations with forbidden values

I already asked this question in the mathoverflow forums, but it seems I won't get an answer as fast as I need one. So I'm moving the thread here. Besides, maybe it isn't as hard as to post it there. ...
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1answer
13 views

All possible types of permutation.

A permutation $ \sigma \in S_{10} $ satisfies the conditions $$ \forall_{1 \le i \le 29} \sigma^i \neq id, \sigma^{30} = id $$ Determine all possible types of the permutations. Give me a hand.
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1answer
18 views

Finding permutation $a$ given $b$ and conjugate $a^b$

Normally we define a conjugate relationship as $$a^b = b~a~b^{-1}$$ But I don't know how to find $a$ given that we know $b$ and $a^b$.
1
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1answer
30 views

What is the minimal cardinality for a generating set of the permutations?

I want to find the minimum number of permutations so that all other permutations can be obtained by multiplying the permutations of this set (taken in any quantity). In other words, I am looking for ...
0
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1answer
11 views

Number of subsequences in a string

I know this might be one of the silliest questions out there but I'm going ahead and ask it here since I've lost practice in mathematics. I have been reading that the number of subsequences in a ...
0
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0answers
14 views

conjugated permutations as to solve

We have: Niech $\sigma = (13624)(587)(9), \tau=(15862)(394)(7) $ Determine such permutation $\alpha$ that $ \alpha \sigma \alpha^{-1} = \tau$ How much are they?
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1answer
24 views

Order of a permutation divides n in Sn

Let $\theta \in S_n$, and for any $k \in \mathbb{N}$, either $\theta^k = I_{I(n)}$ or $\theta^k$ has no fixed elements. Show that $o(\theta) | n$. $I_{I(n)}$ denotes the identity. I'm completely ...
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1answer
28 views

Question in permutations

When we use this law? And in any case we use it? Thank you and I wish clarification.
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1answer
27 views

Permutations and their cycles [closed]

What is the probability that k given elements belong to the same cycle in random permutation ? Thank you in advance.
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0answers
42 views

Prove probing to be permutation

So I have been taught that probe sequences (h(k, 0), h(k, 1), ... , h(k,m - 1)) are meant to be a permutation (0, 1, ... ,m - 1), but how does one prove that? I was asked this question in an ...
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2answers
31 views

Probability, why is this wrong? (Combinations and Permuations)

Why is this the wrong approach to solve this problem? "There are 65 students. 20 of them are sophomores, 20 are freshmen, 15 are juniors and 10 are seniors. When picking a 4 student committee, ...
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1answer
24 views

N Boxes and M babies question.

There are N boxes placed in a straight line. Adjacent boxes are separated by 1 unit. The Babies which are a total of M in number decide to play in this arena of boxes by moving from one box to ...
2
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2answers
22 views

In how many ways can a coat be chosen such that exactly one person picks up the correct coat?

There are n people at a party. At the end they each take a coat at random. a) How many ways can coats be chosen such that no person picks up their own coat/what is the probability that no person ...
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1answer
33 views

Find the number of elements of order 3 in $S_7$

I understand that there are two cycles of length 3, $(i,j,k)(a,b,c) \in$ $S_7$. However, I'm quite stumped in figuring out the logic behind these steps, leading to the answer : Number of distinct 3 ...
0
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1answer
20 views

In $S_6$, write the result as a product of disjoint cycles and then in the 2-row form.

(a) $(1,2,4)(4,3,5)(2,4)(1,2,4)^{-1}$ In the solution for this question, my professor has the product of disjoint cycles written as (1,3,5)(4,1). How would this make sense when disjoint cycles are ...
0
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1answer
18 views

permutations combinations

Q1. Total number of permutations of k diferent things , in a row , taken not more than r at a time(each thing may be repeated any no. of times) is equal to Q2. A teacher takes 3 children from her ...
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1answer
26 views

Show $\alpha^m = \varepsilon$ working with permutation groups

Show that $\alpha^m = \varepsilon$ using $\alpha^\ell (a_i) = a_{(i+\ell) \bmod{m}}$ where $\alpha = (a_0 a_1 \dots a_{m-1}) \in S_n$ a permutation group. I've been working on this problem but can't ...
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1answer
28 views

How to generate a single instance of multichoose (stars and bars)

So we know that if I have $k$ balls and $n$ buckets, I have $\binom{n+k-1}{k}$ unique ways to allocate the balls. Let's say $n=4$ and $k=2$ then I have $\binom{5}{2}=10$ ways. All possible allocations ...
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1answer
125 views

Pixel Permutations

How many possible arrangements of pixels can a 1024x768 pixel screen display if the color of a pixel is determined by mixing 3 values: red, green, and blue, ranging from an intensity of 0 to 255? The ...
2
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1answer
85 views

Number of possible permutations of n1 1's, n2 2's, n3 3's, n4 4's such that no two adjacent elements are same?

Given n1 number of 1's, n2 number of 2's, n3 number of 3's, n4 number of 4's. form a sequence using all these numbers such that two adjacent numbers should not be same. I have tries lot of things ...
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0answers
17 views

Permutation of conjoined faces in regular polygon with diagonals

I've been doing some study on relationships in polygons, right now, regular polygons. I've been trying to find relationships between the diagonals, angles, faces, vertices, and primarily conjoined ...
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3answers
87 views

Permutations and Combinations? 3 digit number…

1) Make a 3 digit even number without repeated digits, using 0, 4, 5 , 6, 7. Also the first digit cannot be 0. 2)Arrange 12 books in a line, 4 of which are english, 3 of which are science, and 5 ...