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

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40 views

Subgroups of $S_4$ generated by cycles

I am new with abstract algebra and I trying to find all the subgroups of $S_{4}$ generated by the cycles : a) $(13)$ and $(1234)$ b) all cycles of length $3$ I am not sure how to start so I would ...
4
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3answers
107 views

A question in permutation

Help is needed in solving the following problem. $8$ persons ($A$ and $B$ and $P, Q, R, S, T, U$) are to be seated in $2$ rows ($4$ seats per row). Find the number of ways that $A$ and $B$ are ...
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1answer
36 views

Equation for a systematic permutation

A $6$ digit number is set whereby every digit can be repeated without any constraints. So one can have a number between $000001$ and $999999$. (Zeros on the left are counted). The problem: Generate ...
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0answers
73 views

Is this problem still open or solved?

Problem- Let $n\geq$ and let $T$ be the set of all permutations in $S_n$ of the form $t_k=\prod_{1\leq i\leq k/2}(i,k-i)$ for $k=2,3,4.....(n+1)$. Then find the least integer $f_n$ such that ...
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1answer
28 views

Five digit numbers where each digit can appear up to three times

The question is to determine how many five-digit numbers there are (using the digits 0-9) where each digit can appear up to three times in the number. The total number of numbers that can be made ...
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1answer
31 views

Combinations of percentages.

How would I calculate all possible combinations of given percentages so that none of the combinations is less than 51%? For example one such combination of 24% 23% 21% 17% 8% 7% would be 23% + 24% ...
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2answers
43 views

Combinatorics: Participants in a match

In a tournament, each of the $6$ participants played 2 matches against each of the other participants. What was the total number of matches played during the tournament? So we have a set of 6 ...
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1answer
20 views

Permutation and Combination - Algorithm

Given Data in the problem For I= 1 to 10 print(x) means executing the immediate next line after for loop command 10 times. So here it prints "x" 10 times. Typical simple for loop construct in ...
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1answer
165 views

3 digit odd numbers that can be formed using 0,3,5,7 - no repetition

Q. How many 3 digit odd numbers can be formed using 0,3,5,7, repetition not allowed. WHAT I DID :- 3 x 3 x 1 = 9 For Hundredth place - It can be filled in 3 ways (any of 3,5,7), we cannot use 0. ...
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2answers
16 views

Possible combinations [closed]

I'm trying to write a set of documents on LAMP (Linux, Apache, MySQL & PHP). In this series I have 11 Centos Versions, 3 Apache versions, 5 MySQL Versions & 9 PHP versions. I will be writing ...
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2answers
23 views

Combination problem with distributing

I've been trying to do last exercise, but I can't figure out method to solve it. I read a book and searched for it in the internet, but I couldn't find exactly what I am looking for. Could you guys ...
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0answers
13 views

Cycle evenness and oddness

I have a definition for evenness and oddness like this: e = ordinary product ($pk - pi/k - i$) (when i < k) and p is a permutation. First, what does evenness and oddness represent and where did ...
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2answers
21 views

maximum number of seedlings planted in a 100meter field [closed]

In a square field with side length of the 100 meters, if the distance between 2 adjacent plants must be maintained at not less than 1 meter, then the maximum number of seedlings that can be planted is ...
2
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2answers
31 views

Number of possible eight digit number divisible by 9

An eight digit number divisible by 9 is o be formed by using 8 digits out of 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 without repetition. Find the number of ways in which it can be done. I know divisible rule of ...
0
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1answer
64 views

Number of ways to make n digit number?

Given M digits which are between 1 to 9, Find the number of ways to form N digit number, by repeating one or more given digits such that each of M digits are present in N digit number at least once. ...
0
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1answer
28 views

probability and order question

What is wrong in my solution ? Q: If we have $N$ number of light leds, and the probability of having faulty ones is $R$ (in percentage), what is the probability of having 2 or more faulty light leds ...
4
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2answers
66 views

Is every group a permutation group?

I just read about permutation groups. Before going further this question came up in my mind. Isn't every group a permutation group? The definition says, "one-to-one mappings of a set onto itself is ...
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1answer
18 views

Circular permutation; trouble understanding

I have looked around at MSE and I can't find any explanation to what I'm looking for. I'm trying to understand the second reasoning to the formula $P_c = (n-1)! = \frac{n!}{n}$, where $P_c$ is the ...
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1answer
46 views

Could someone help me out with permutations/combinations?

I need some help understanding how to approach problems with permutations/combinations. Could someone first explain when I should be using combinations and when I should be using permutations? Then ...
0
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1answer
17 views

Permutation question in discrete mathematics. At least 1 out 3 members (P) from a total of 10 members

Im doing a question out of Discrete and Combinatorial mathematics by Grimaldi (4th Edition). Im stuck on one of the questions and am trying to find an alternative way of doing it, that is not in the ...
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1answer
29 views

In S4, find all the even permutation and show that the set of odd permutations isn't stable for binary operations in S4.

I want to find the even permutations of $S_4$ so i am supposed to find the transpositions right? but of what permutation exactly do i find the transpositions? And how do i know which ones are even? ...
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3answers
97 views

Counting problem: generating function using partitions of odd numbers and permuting them

We have building blocks of the following lengths: $3, 5, 7, 9, 11$ and so on, including all other odd numbers other than $1$. Each length is available in two colors, red and blue. For a given number ...
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1answer
15 views

Is my interpretation about this problem on permutation and combination is correct - exactly 3 invitee?

A man has 9 frinds : 4 boys and 5 girls. In how many ways can he invite them, if there have to be exactly 3 girls in the invitees? ...
0
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1answer
35 views

How do i prove this? ( about permutation)

Let $n>1$. Let $\tau \in S_{n+1}$ and $1≦l≦n+1$. Assume that $\tau(l)=l$. Now, define a permutation $\mu\in S_n$ as $\mu(i)=\tau(i)$ if $i<l$ and $\mu(i)=\tau(i+1)$ if $l≦i≦n$. (If $l=n+1$, ...
2
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2answers
26 views

Permutation in PERMUTATIONS

In the word $PERMUTATIONS$.How many ways can I what is the number of permutation so that a vowel word must be between two consonants.a word can be used only for one time.
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2answers
33 views

Combinatorics, how to pick X of one item, and Y of another out of Z total items?

Let's say I have several kinds of bricks. Red bricks, yellow bricks, and blue bricks. If I have infinite bricks, but am only selecting a group of 15 bricks, what is the chance I pick 7 red, 5 yellow, ...
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2answers
386 views

How many ways to seat 4 couple and 2 single around a round table

How many ways to seat 4 couple and 2 single around a round table, provided that each couple will sit together
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3answers
40 views

How to solve this combination problem quickly?

In how many ways can 3 men and their wives be made stand in a line such that none of the 3 men stand in a position that is ahead of his wife? What is the best way to tackle such problems? ...
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0answers
21 views

Number of Permutation with Constraints

While thinking about a research question, we came across the following problem - what are the total number of permutations of the first $N$ natural numbers, where each number satisfies the constraint ...
3
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1answer
35 views

Good Book on Permutations and puzzles

I need to study about permutations to mathematically analyze scrambling of digital images. Do you know any good books on this matter ??
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1answer
20 views

Verify my thought process on permutations

If there are $15$ distinguishable objects; all will be placed into $2$ boxes. There needs to be at least one object in each box. How many ways can you place these objects into the $2$ boxes? Tried ...
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2answers
34 views

Permutation and combination related question

My question is: Starting from Washington, DC, how many ways can you visit 5 of 50 state capitals and return to Washington? I tried to solve it, Firstly, we should choose 5 states from 50 countries ...
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1answer
32 views

Group actions and permutation representation

Im trying to solve this problem from Dummit & Foote: Let $G$ be a transitive permutation group on the finite set $A$. A block is a nonempty subset $B$ of $A$ such that for all $\sigma\in G$ ...
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3answers
48 views

Is there a closed form for a sum $nPk +(n-1)Pk + (n-2)Pk + … + kPk$?

I would like to know if there is some closed form to solve for a sum in the form: $nPk +(n-1)Pk + (n-2)Pk + ... + kPk$ For instance, if $n=7$ and $k=2$: $7P2 + 6P2 + 5P2 + ... + 2P2$ = ...
0
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1answer
21 views

What are the total number of ordered permutations of a list of elements (possibly repeated)?

This question is a part of a TopCoder problem. I am learning algorithms, and just got stuck at this (not homework). Suppose we have a set $A$ of integer elements, such that $n(A) = a$ (number of ...
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2answers
24 views

Arrangement of 5 letter words

There are 26 letters in the alphabet. How many 5-letter words can you make if you can repeat letters, but cannot have two letters in a row that are the same? My strategy: Since there are 26 letters, ...
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2answers
46 views

Combinations and Permutations: Number of ways of taking out 1 $ bills

Can A has N 1 $ bills. Can B is empty. At each step you can either take a bill from can A or put a bill you already have into can B. You can choose to keep some bills in your hand and take some more ...
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0answers
32 views

Probability of a number of weighted items being allocated to the same bin

I have the following (probably classic) combinatorics problem: There are $n$ bins that can hold $k$ items each, and a total of $r = n\,k$ items. The items have weights $w_1 > w_2 > \dots ...
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2answers
58 views

Why does the wording of how many ways can a photographer 6 people from a group of 10 ask for permutations and not combinations?

Note: Please do not post the mathematical notation for binomial coefficient or "n choose m" or anything related to that. The chapter where that is introduced comes much later. Therefore I would not ...
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2answers
22 views

Amount of ways to schedule activities using combination or permutation.

I'm trying to review for Probabilities and Statistics and came upon this Question. If one needs to schedule a job interview for someone who wants to teach at a school. For the day of the interview, I ...
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0answers
39 views

Indexing ranked permutations into other ranked permutations

Consider all permutations of 0, ..., n-1 under some ranking R. Given two ranks, i and j, what is the rank of the permutation that results from applying the i'th permutation to the j'th permutation? ...
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34 views

View a group acting faithfully and transitively on a set $X$ as a subgroup of a wreath product.

I'm studying algebra and I saw that given $H$ group of permutations of a set $\Delta$ and $K$ group of permutation of a set $\Omega$ we have that the wreath product $H\wr K$ is a group of permutations ...
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2answers
100 views

How many hands are there with exactly 5 hearts after drawing 7 cards from a deck? [closed]

Draw 7 cards from a deck of 52 cards. How many hands are there with exactly 5 hearts? Will it be something like $$\frac{1!}{(52!51!50!49!48!)\cdot(7!6!5!4!3!)}$$ I'm pretty sure its wrong, any help ...
0
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1answer
59 views

How many ways can we put $5$ red balls, $4$ green balls and $3$ white balls into $12$ slots?

How many ways can we put $5$ red balls, $4$ green balls and $3$ white balls into $12$ slots? Would it be $12!$ or $\dfrac{12!}{5!4!3!}$? I'm confused here.
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0answers
67 views

How many Possible Combinations exist?

I have $120$ coins and $21$ buckets. Each bucket can hold $0$ to $20$ coins. How many possible coin/bucket combinations are there?
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2answers
31 views

Proving $ \sum_{r=0}^{n} \frac{1}{r+1} \binom{n}{r} = \frac{1}{n+1} (2^{n+1} - 1) $

I'm stuck at proving the following. $$ \sum_{r=0}^{n} \frac{1}{r+1} \binom{n}{r} = \frac{1}{n+1} (2^{n+1} - 1) $$ This is what I have so far. $ \sum_{r=0}^{n} \frac{1}{r+1} \binom{n}{r} = (1) ...
0
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1answer
47 views

Problem finding the number of r-element multi-subsets of the multi-set $M=\{ a_{1},a_{2},…,a_{n},m.b \} $

Let $m,n,r \in \mathbb{N}$. Find the number of $r$-element multi-subsets of the multi-set $$M= \{ a_{1},a_{2},...,a_{n},m.b \} $$ when $r \leq m,r\leq n$. Below is the given answer. ...
2
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0answers
52 views

Permutation & combination for creating housie tickets

A game called housie (similar to Bingo) is played in India. This game is played by a group of people based on a few rules. I need to know how many unique tickets can be printed in one session of a ...
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1answer
34 views

Probability of being selected twice in a week given a set of n people?

Let's say a child is selected out of a group of 10 students each day to stay after school and help clean the classroom. What is the probability that a particular child is selected exactly twice during ...
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1answer
12 views

number of rectangles (including squares)

I have a grid of squares of unit length each with value 0 or 1. I want to count the number of squares or rectangles that can be made within this grid no taking the unit sqaures with value 1. If the ...