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

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In how many ways can 4 red, 3 blue and 2 green balls be arranged? [closed]

In how many unique ways can 4 red, 3 blue and 2 green balls be arranged if they are indistinguishable aside from color?
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2answers
22 views

Limiting how often an element can repeat

Say I have two elements (0, 1) and I want to find the number of permutations of sequences of, say, length 10. However, I want to limit it so that "1" can never appear more than twice in a row, with no ...
2
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2answers
52 views

Can the image of a set under a permutation be a proper subset of the set itself?

I'm working on some exercise in Fraleigh's "A First Course in Abstract Algebra" and one of them involves permutations under which the image of a certain set is a subset (proper or improper) of the set ...
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2answers
57 views

Ordered pairs of permutations in symmetric group

How many ordered pairs $\left(\alpha_1,\alpha_2\right)$ of permutations in symmetric group $S_n$ that commute: $$\alpha _1 \circ \alpha _2 = \alpha _2 \circ \alpha _1\,,$$ where $\alpha _1, \alpha _2 ...
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0answers
22 views

possible number of arrangements for a group of 6 words

How many ways (possible combinations without repetition) can we arrange these words? ServiceInfo, TokenInfo, AccountInfo, DeviceInfo, LocationCoarseInfo, LocationPreciseInfo
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1answer
27 views

Spectral Radius of a Sum of Permuted Matrices

Consider $n$ real, symmetric, and positive semi-definite matrices as: $A_1,A_2,\cdots,A_n$. These matrices are convertible to each other under appropriate permutation ($A_i(p_i,p_i)=A_j$). Moreover, ...
2
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1answer
25 views

Selecting n balls from N - Cumulative Distribution Function

I am having difficulty with the following question: Suppose that N balls labelled $\{1, 2, . . . , N\}$ are placed in a box, and n balls ($n ≤ N$ ) are randomly selected without replacement. Define ...
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1answer
49 views

Count Orbits and stabilizer

Let $X$ be the set $\mathbb{Z}_9\times \mathbb{Z}_9$ and let $U_9$ denote the group of invertible elements in $\mathbb{Z}_9$. The group $G$ acts on $X$ defined by $u(x,y)=(ux,uy)$ where $u\in U_9$ and ...
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2answers
29 views

Left cosets of $A_6$ in $S_6$

Which may be the all of left cosets of $A_6$ in $S_6$? $\{A_6,(156)A_6\},\{A_6,(34)A_6\},\{A_6,(42)(35)A_6\}, \{A_6,(46523)A_6\}$ or $\{A_6\}$ I dont understand why the answer is $\{A_6,(34)A_6\}$ .I ...
2
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1answer
30 views

Permutation & Combinations - Distribution

The number of ways in which n distinct things can be distributed among n people so that at least one person does not get anything is 232. Find n. I think every object has (n-1) option. So (n-1)^n=232. ...
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2answers
24 views

Find the number of ways this can be arranged in which no 2 women and no 2 men sit together given 4 men and 3 women are seated in a dinner table?

Find the number of ways this can be arranged in which no 2 women and no 2 men sit together given 4 men and 3 women are seated in a dinner table? @Edit: They are seating in a row dinner table I have ...
3
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1answer
34 views

Group $G$ acting on $\Omega$ such that each $\alpha \in \Omega$ has unique $p$-element fixing $\alpha$.

Let $G$ be a group acting on a set $\Omega$ and let $p$ be a prime. Suppose that for each $\alpha \in\Omega$ there is a $p$-element $x \in G$ such that $\alpha$ is the only point fixed by $x$. If ...
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3answers
61 views

In how many words the letter of word RAINBOW be arranged so that only 2 vowels always remain together?

My Approach: RAINBOW has 4 Consonants and 3 vowels. Out of 3Vowels 2 vowel are selected and arranged in 3P2 ways and the rest letters are arranged in 5! ways(1vowel and 2 consonants) The ...
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2answers
37 views

In how many ways the letters of the word RAINBOW be arranged such that A is always before I and I is always before O.

I research some sites and books and i found these this approach helpful but could not understand a bit. Approach: All the 7 letters of the word can be arranged in 7! ways. and 3particular letters ...
3
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3answers
48 views

Number of Non - Decreasing functions?

Let A={1,2,3.....10} & B={1,2,3....20}. We have to find the number of non decreasing functions from A-->B. What I tried :No. Of non decreasing functions = (Total functions) - (Number of ...
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1answer
71 views

Find the sum of all 4 digit numbers which are formed by the digits 1,2,5,6?

I have researched and found 2 approaches but haven't understood both.Can anyone explain it clearly or probably with any real world example? Approach 1 Four digit numbers $ = 4 \cdot 3 \cdot 2 ...
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1answer
34 views

Permutations where no partial sum is divisible by 3 (contest question)

A permutation of the integers $1901,1902\dots 2000$ is a sequence in which each of those integers appears exactly once. Given such a permutation, we form the sequence of partial sums $$s_1 = ...
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2answers
43 views

Correctly calculating permutations and combinations without duplicate patterns

Given 16 balls each numbered 1 through 16, and 5 glass tubes numbered 1 through 5; how many ways are there to slot all 16 balls into the glass tubes, selected one at a time, with the only condition ...
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3answers
68 views

In $S_7$, find the permutation $x$ that satisfies the condition $x^2 = (1,2)(3,4)$.

In $S_7$, $X^2 = (1,2)(3,4)$. What is the permutation $X$ that satisfies the given condition?
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1answer
50 views

How to understand the set of permutation representations of a group $G$?

In Algebra by Michael Artin, Chapter 6, page 182 (second edition, Pearson), Proposition 6.11.2 states that there exists a bijective correspondence between operations of a group $G$ on the indices set ...
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2answers
41 views

Conjugacy in $S_n$ with composing permutations left to right vs. right to left

I realize there are two conventions for composing permutations. Left to right: $(1\ 2)(1\ 3) = (1\ 2\ 3)$ Right to left: $(1\ 2)(1\ 3) = (1\ 3\ 2)$ Among others, Dummit and Foote and Contemporary ...
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1answer
17 views

Question pertaining to permutation.. finding ways of letters being rearranged [closed]

Q: In how many is the N somewhere to the left of the u if the letter of the word NUMBER being arranged?
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0answers
55 views

A fashion victim puzzle

Consider $n \in \mathbb{N}$ fashion-sensitive kids, each wearing a T-shirt; for simplicity, kid $i \in \{1, \ldots, n\}$ initially wears shirt $i$. Tastes over the shirts are summarized in an $n ...
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1answer
47 views

Finding the n-th arrangement of items with repetitions [duplicate]

I'm new to Stackexchange and maybe I do not have the correct mathematical terms for the question I'm about to ask. I'm given a multiset of given size $N$ which consists of zeros and ones. Example: ...
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1answer
37 views

A Permutations/Combinations Question and Inquiry on Good Source for Studying The Concept

Lets say a burger joint offers options for customizing burgers. There are 3 types of meats and 7 condiments. A burger must include meat but may include as many or as few condiments as the customer ...
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0answers
55 views

How many anagrams of a given word exists with constraints

I saw many questions about anagrams here, but neither one fits my needs. Let's say we have the word MISSISSIPPI. I need to find the count for those anagrams that meet the criterias as follows: ...
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2answers
44 views

A three-character password, how many different passwords are possible?

a three-character password consists of 2 different digits between 0 and 9 inclusive. and 1 letter of the English alphabet. the letter must appear as first or second character, how many different ...
2
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1answer
20 views

Signum or parity of a transposition is $-1$

The definition of signum $\alpha$ is given by $$sgn(\alpha)=(-1)^{n-t}$$ where $\alpha=\beta_1\dots\beta_t$ a complete factorization of disjoint cycles. If $\alpha$ is a transposition, then it moves ...
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2answers
83 views

How many permutations of the letters AEIOU contain the strings EA and UO?

So here is our "word" AEIOU. Then we need to find how many permutations contain EA and UO. Then how many contain AE and EI and how many end with O. I know how to figure out some of these problems ...
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1answer
38 views

Basic probability - lottery type question

I know this might sound really basic, but my maths/stats knowledge has gone very rusty over the years... Maybe I can get a head start here. If I ask my user to choose 5 numbers, how do I calculate ...
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1answer
21 views

Total number of possible permutations [closed]

How many ways can 10 people be seated in a row, so that a certain 2 of them are not seated next to each other.
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0answers
37 views

Composing a permutation with a transposition and length

Let $\pi$ be an element of the permutation group $S_n$, such that, when it operates on the ordered set $\{1, 2, \ldots , N\}$, the ordered set that it produces $\{k_1, k_2, \ldots , k_N\}$ has two ...
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0answers
30 views

Minimal polynomial of endomorphism of permutation module

Let $G$ be a transitive permutation group on a set $\Omega$. If $n$ is the degree and $M\in\mathbb{Z}^{n\times n}$ is a symmetric matrix that is also contained in ...
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2answers
80 views

Ordered Arrangement of Books

A shelf has $10$ distinct books of which $3$ are Math,$ 4$ are English and $3 $ are Science books. In how many ways can you arrange these books such that all English books will be placed in the ...
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1answer
54 views

A team has 13 members suppose seven are women and six are men? How many groups?

I'm having trouble figuring out the permutations and how to properly multiply them together for this problem. A computer programming team has $13$ members. a.) How many ways can a group of seven ...
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0answers
48 views

Use of permutation/combination in Geometric problems

There are $p$ points in space, no four of which are in the same plane with exception of $q$, which are all in the same plane. Find out how many planes there are each containing three of the points? ...
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2answers
33 views

Clarification of a concept in Permutation

Statement 1 No. of ways in which $(m+n+p)!$ different things can be divivded into different groups containing m,n & p things respectively. is $(m+n+p)!/m!n!p!$ Statement 2 If $m=n=p$ and the ...
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4answers
81 views

How to find number of numbers formed with given digits?

Question is Find the number of numbers of five digits that can be made with the digits of the number 1203210. Can you please explain the problem? I did not understand it. Although one asked similar ...
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3answers
42 views

A problem on Permutation/Combination.

Q.How many ways no.s less than 10000 can be made with digits $1,2,3,0,4,5,6,7$? My attempt: The no.s should be of $4$ digit. It cant start with $0$ Then,the no.s of no.s possible should be ...
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2answers
26 views

Proof of a formula related to permutations and combinations involving geometrical figures

How to prove that the number of triangles that can be formed by joining the angular points of a polygon of n sides as vertices are$\dfrac{n(n-1)(n-2)}{6}$?
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2answers
67 views

Missionary and Cannibal problem

I got an interesting problem yesterday (Yes, for homework, but it seems like this is on topic) The problem goes like this: Three missionaries and three cannibals wish to cross a river. There is a boat ...
2
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1answer
57 views

There are 3 workers in a company that has 5 working days in a week.

There are 3 workers in a company that has 5 working days in a week.In how many ways can the 3 workers take leave/rest if no two workers can take leave on the same day. Attempt: The first worker can ...
0
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1answer
25 views

A problem in permutation/combination

Q.A boat is to be manned by eight men,of whom $2$ can only row on bow side and $1$ can only row on stroke side,in how many ways can the crew be arranged? I approached the problem in the following ...
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1answer
16 views

How to calculate route variations/permutations

If I have 5 trucks and 10 deliveries to make per truck, that's 50 deliveries total, but how many different route variations could there be? You could give each truck the list of deliveries and they ...
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2answers
81 views

Why does $\sum_{\sigma\in S_n}q^{\ell(\sigma)}=\frac{(1-q)(1-q^2)\cdots(1-q^n)}{(1-q)^n}$?

This is a known result, but I can't find a proof. Why does $$ \sum_{\sigma\in S_n}q^{\ell(\sigma)}=\frac{(1-q)(1-q^2)\cdots(1-q^n)}{(1-q)^n}? $$ Here $\ell(\sigma)$ is the length of $\sigma$, ...
0
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1answer
23 views

Sampling without replacement from unknown sample size

Five mice are chosen (without replacement) from a litter, three of which are tagged $A$, $B$ and $C$. The probability that all three tagged mice are chosen is twice the probability that $A$ is the ...
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1answer
20 views

Number of ways 1a,1b,5 can add up to n (with this being a permutation)

This problem is on my homework. A vending machine dispensing books of stamps accepts $\$ $ 1 coins, $ \$1 $ bills and $ \$5 $ bills. A) Find a recurrence relation for the number of ways to deposit n ...
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3answers
52 views

Pick $x$ out of $y$ objects. Match $n$ picks.

Computer randomly picks a group of 6 objects out of 30, no repetitions. User than picks $6$ objects out of those $30$, also no repetitions. What are the odds of the user getting $3$ of his picks to ...
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2answers
24 views

How many bit strings of length 10 contains…

I have a problem on my home work for applied discrete math How many bit strings of length 10 contain A) exactly 4 1s the answer in the book is 210 I solve it $$C(10,4) = \frac{10!}{4!(10-4)!} = ...
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0answers
55 views

Why does $\operatorname{SL}_2(3)$ only yield even permutations?

$\newcommand{\pa}[1]{\left(#1\right)} \newcommand{\pamat}[1]{\left(\begin{array}{cc} #1 \end{array}\right)}$ In an exercise lesson for Algebra 3, we were proven that the special linear groups over ...