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

learn more… | top users | synonyms

0
votes
2answers
29 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, ...
0
votes
2answers
48 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 ...
0
votes
0answers
33 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 ...
1
vote
2answers
544 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 ...
0
votes
2answers
25 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 ...
1
vote
0answers
42 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? ...
1
vote
0answers
36 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 ...
0
votes
2answers
124 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
votes
1answer
60 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.
0
votes
0answers
90 views

Number of ways to put $120$ coins in $21$ buckets, if each bucket can hold $0$ to $20$ coins

I have $120$ coins and $21$ buckets. Each bucket can hold $0$ to $20$ coins. How many possible coin/bucket combinations are there? Here is where I'm running into trouble - I know there are $21$ ...
0
votes
2answers
33 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
votes
1answer
56 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
votes
0answers
100 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 ...
1
vote
1answer
38 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 ...
0
votes
1answer
16 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 ...
1
vote
1answer
34 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. :)
0
votes
0answers
25 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 ...
1
vote
3answers
78 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 ...
1
vote
0answers
23 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
votes
1answer
26 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
votes
1answer
36 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 ...
0
votes
0answers
20 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 ...
1
vote
1answer
36 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 ...
0
votes
1answer
67 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 ...
0
votes
1answer
14 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.
0
votes
0answers
70 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 ...
2
votes
0answers
24 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 ...
0
votes
0answers
56 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 ...
0
votes
1answer
29 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?
0
votes
0answers
50 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 ...
0
votes
3answers
55 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 ...
0
votes
2answers
26 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 ...
0
votes
1answer
32 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 ...
1
vote
2answers
116 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. ...
0
votes
0answers
16 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 ...
1
vote
2answers
36 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
votes
2answers
169 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 ...
1
vote
2answers
106 views

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

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 ...
2
votes
1answer
35 views

Possible number of arrangement.

Question: How many cars are there with number GJ-X-AB-abcd. GJ and A are constant.X is digit between 1 to 9, B is english alphabet and abcd is 4 digit number.(a can be zero) My Efforts: It is but ...
0
votes
1answer
25 views

Find the possible number of assignments?

S students, I interviewers, each student has to undergo R interviews, each interviewer can interview at max X students. No student interviews with an interviewer more than once, and no interviewer ...
1
vote
2answers
25 views

Permutations and Sample Spaces

Suppose 3 cars can either turn left $(L)$, turn right $(R)$, or go straight $(S)$. I need to find the sample space for all the possibilities but I am not sure how to do that. I know that for 3 cars ...
-1
votes
3answers
226 views

How many distinct permutations can be made from the letters of the word IN F IN IT Y? [closed]

How can I determine how many distinct permutations can be made from the letters of the word infinity ?
0
votes
0answers
23 views

Cyclic Permutation of identical objects

I just want to confirm if this formula for cyclic permutation of identical objects is correct. If there are n objects of which p are identical of one kind, q are identical of second kind, r are ...
2
votes
2answers
121 views

A Question on distribution numbers

This is a question from the book Combinatorics -a problem oriented approach which states: Q.1 Find the no. of distributions of a set of distinct balls into a set of distinct boxes, if no boxes can ...
0
votes
0answers
20 views

How do we deal with such arrangement problems?

15 different balls are kept in a straight line. Then their order is changed such that no ball is adjacent to a ball which it was adjacent to earlier. In how many ways can this task be ...
2
votes
1answer
108 views

What does the factorial of a negative number signify?

I understand that the factorial gives the number of arrangements. For example: the factorial of zero i.e. an empty set ( doesn't occur) is 1. As the empty set can be arranged only in 1 way - i.e. by ...
2
votes
0answers
37 views

What is the motivation behind the study of pattern-avoiding permutations?

There is a ton of research on pattern-avoiding permutations (permutations that do not contain some designated permutation pattern). We're figuring out how to enumerate them, what random ones are ...
0
votes
0answers
55 views

How many arrangements (correct and incorrect) possible with cube puzzle pieces in a particular unfolded form?

I am trying to do a computer program for arranging cube puzzle pieces in an unfolded form. A cube can be unfolded into 11 forms or nets. I have chosen a single net for now for simplicity purposes and ...
1
vote
2answers
46 views

Closed form sum for the series given below?

Does the following series have a closed form sum? $$f(n,r) = \sum_{i=0}^n \binom{r+i}{r}$$
0
votes
1answer
52 views

How to use group theory to solve larrys square iphone app

There's a 2 d version of rubiks cube on apple app store. How can group theory give an algorithm to solve the iPhone app:larry's square.