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

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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
344 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
33 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
14 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
19 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
24 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
28 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
45 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 $k=2$: $7P2 + 6P2 + 5P2 + ... + 2P2$ = ...
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1answer
20 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
29 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
27 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
20 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
34 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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0answers
33 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
85 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 ...
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1answer
31 views

Using Maple, to calculate how many times does the digit 7 occur in the numbers from 1221 up to 12021? [closed]

I need to write a program in Maple to calculate how many times does the digit 7 occur in the numbers from 1221 up to 12021? Please help. Thanks.
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1answer
54 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
39 views

Permutation/Combination Question!

A club is forming a committee to plan its annual Holiday Dance. One person will serve as Chair of the committee, another will be Vice-Chair and there will be two other members. Is this an example of a ...
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0answers
42 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
30 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) ...
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1answer
35 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. ...
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0answers
39 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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2answers
31 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
11 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 ...
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1answer
17 views

How many words can be formed by taking 4 letters at a time from the letters of the word 'MORADABAD'?

What I tried was: (9P4)/3!*2! This gave me a wrong answer (since the answer is 626). I'm unable to make use of the hint provided in my book: "make cases". Any help would be appreciated. :)
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0answers
13 views

arrangement with inclusion-exclusion

How to solve the following problem using inclusion -exclusion principle? Given n and a letter C,how many possible words of length n can be formed that are with no two consecutive C in the word. For ...
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3answers
77 views

Problem proving $ P_{r}^{r} + P_{r}^{r+1} + … + P_{r}^{2r} = P_{r}^{2r+1} $

Show that $$ P_{r}^{r} + P_{r}^{r+1} + ... + P_{r}^{2r} = P_{r}^{2r+1} $$ where r is a nonnegative integer. This is what I've come up with so far but I'm not sure how to continue. I know I need to ...
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0answers
19 views

The number of ways to schedule six activities

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 ...
0
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1answer
19 views

arrangement with condition

Given n and a letter C,how many possible words of length n can be formed that are with no two consecutive C in the word. For example,if n=3, C='b',then the word bcb,ccc,aab do not have any ...
2
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1answer
28 views

Algebra - proof verification involving permutation matrices

Theorem. Let $\textbf{P}$ be a permutation matrix corresponding to the permutation $\rho:\{1,2,\dots,n\}\to\{1,2,\dots,n\}$. Then $\textbf{P}^t=\textbf{P}^{-1}.$ Proof. First note the following ...
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0answers
14 views

count the permutation which have $k$ maxima

I need some help for the following homework question. A permutation $P (\pi_1\pi_2...\pi_n)$ of {$1,2,...,n$} is given. We say that $j$ is a maxima of $P$ whenever $\pi_j$>$j$. How can I find ...
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1answer
33 views

Cycles of odd length: $\alpha^2=\beta^2 \implies \alpha=\beta$

Let $\alpha$ and $\beta$ be cycles of odd length (not disjoint). Prove that if $\alpha^2=\beta^2$, then $\alpha=\beta$. I need advice on how to approach this. I recognized that $\alpha,\beta$ are ...
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1answer
28 views

Solving an equation involving factorial notation

I was given this problem in the text book: $$\frac{(n+4)!}{(n+2)!} = 6$$ $$n \in I $$ Since the textbook doesn't have the solution, I'm wondering if I'm right: $$\frac{(n+4)!}{(n+2)!} \Rightarrow ...
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1answer
12 views

String Permutation

If we have the string ab, would abab be a permutation of ab? It seems that a permutation is a rearrangement of things but only within the things in our set. In this example, that set is ab.
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0answers
62 views

What combination of the 16 listed digits make two numbers N and M that fit in the equation M=2*N

Here's the whole problem: Consider the list of 16 digits 2; 2; 3; 3; 4; 4; 5; 5; 6; 6; 7; 7; 8; 8; 9; 9: Can these digits be used as the digits of two numbers, M and N, with M = 2N? If yes, produce ...
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0answers
20 views

Total number of possible graphs in a network with $m$ edges and $n$ vertices?

How do you calculate the total number of possible graphs in a network with $m$ undirected edges and $n$ vertices? No self-loops. For instance, if I have a network with $7$ vertices in it, I want to ...
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0answers
35 views

How to compute the topological entropy of a permutation?

I have a permutation, say as ${4,1,7,2,3,5,6}$, given by its induced matrix. According to this paper (Proposition 11 on p. 82), To compute its topological entropy, one can compute the ...
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1answer
27 views

permutations and combinations very tough

In how many ways can the letters of the word 'arrange' be arranged if the two r's and the two a's do not occour together?
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0answers
43 views

Distributing balls in boxes.

In how many ways can $n$ identical balls be distributed amongst $m$ different boxes given that a box can have any number of balls(from $0$ to $n$)? What I've tried is using multinomial theorem to ...
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3answers
53 views

Need help with flaws in statistical reasoning

The problem is as follows - there are three couples and six chairs in a row. The six individuals are seated at random. What is the chance that at least one couple will be seated together? Here's my ...
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2answers
23 views

Stuck with divisibility test in Permutations

How many 5 digit numbers can be formed using digits 0 to 7, divisible by 4, if no digit occurs more than once in a number. 1480 780 1360 1240 None Of These I could calculate the ...
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1answer
28 views

Permutation with atleast n unique characters

I came across this question on Google APAC 2015. I am slightly weak with permutations. The problem goes like this: There is a password. We know the length of the password and the characters used ...
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2answers
26 views

Permutation and Combination for 6-digit numbers contain exactly 4 different digits

I found a question online. How many 6-digit numbers contain exactly 4 different digits ? My Solution is : There are 6 digits and 4 needs to be unique so either 2 digits can be same or 3 can be same. ...
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0answers
11 views

Number of Different Combination Possible?

You are given number of places as m and number of digits as n.You have to fill those m places in such a way that each digit appears atleast one time. For Example Given m as 4 and n as 3 so you have ...
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2answers
29 views

Order of a permutation

What does the order of a permutation actually mean? I accept the fact that it is the l.c.m. of the lengths of the cycles in its cycle decomposition, but I don't really have an intuition for what the ...
2
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2answers
107 views

Hat Matching Problem Expectation

I have an interesting problem in the context of the hat matching problem: There are n people with hats at a party. Each person randomly grabs a hat. A match occurs if a person gets his own hat. I'd ...
2
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2answers
82 views

How many ingredients does he use if the burger has 99 varieties?

A burger-shop keeper says that he has 99 varieties. My questions is: how is it possible to have 99 varieties? How many ingredient does he uses? I am saying this because there is no number, whose ...