# Questions tagged [permutations]

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

12,804 questions
Filter by
Sorted by
Tagged with
24 views

### What is the probability of at least one coincidence after a permutation?

Imagine we have N distinct and ordered elements. (1, 2, 3, 4, 5, 6, 7) # Example with 7 elements. And we permute them randomly, for example.... ...
• 391
24 views

### Combinatorics -- committee of 4 problem

The problem at hand is that we want to select a committee of 4 people from a pool of 6 men and 7 women (this problem is from a textbook, I didn't come up with it). We want to know how many ways we can ...
25 views

### Confusion with problem regarding 3-letter strings created from a 5-letter alphabet

I'm taking a discrete math course in university right now and we're studying permutations and combinations as one of the chapters. The question I'm confused about states that given a 5-letter alphabet,...
91 views

### Number of binary strings of length $56$ vs number of permutations of English alphabet

This is exercise $1.2$ in Nicholas Loehr's book "Combinatorics". Which is larger: the number of binary strings of length $56$, or the number of permutations of the English alphabet ($26$ ...
• 2,301
17 views

### Question involving Permutation and Combination [closed]

You have to choose 5 out of 7 items to arrange, 3 of which are the same. Solve this question.
1 vote
44 views

### Why is the traditional proof of the formula for permutations by the multiplication rule not formal?

The traditional, most common proof of $_nP_n = n!$ is by the multiplication rule: There are $n$ choices for the first position, $n-1$ for the second, and so on until there is only one choice for the ...
• 296
40 views

### A question regarding a permutation in $S_n$

Let $\sigma\in S_n$. For each $i\in\{1,2,\ldots,n\}$ let $k_i$ be the smallest positive integer such that $\sigma^{k_i}(i)=i$. Suppose now that $k_1,\ldots,k_n$ are all even. Is it true that $n$ must ...
• 4,757
43 views

### Combination problem : 6 Schools , three sports.

Six schools participate in a youth sports conference and each school is represented by three players a cricketer, a soccer player, and a hockey player. It is required to select a committee of six ...
• 5,954
64 views

36 views

### Application of Permutation

I have this problem below: In a row of six houses (numbered, in order, 1–6) live six married couples, each consisting of a woman and a man, a couple in each house. Each of the women also has (exactly) ...
25 views

### Let $I$ be the collection of all involutions (for all $n \geq 0$). Find the EGF for $I$. [closed]

A permutation $\pi$ of $[n]$ is said to be an involution if its cycle decomposition consists of only $1$- or $2$-cycles. Let $I$ be the collection of all involutions (for all $n \geq 0$). Find the EGF ...
47 views

### Finding a simple graph such that its automorphism group equals the subgroup of $S_3$ generated by a 3-cycle

I have found that the subgroup of $S_3$ generated by a 3-cycle is $\{e,(123),(132)\}$ where $e$ is the identity but I can't find any graphs that have this group as their automorphism group. I am a ...
• 21
111 views

• 19.9k
1 vote
31 views

### Formulas to calculate the number of inversions for a permutation of n length: (help solving)

While reading Donald Knuth's "Sorting and Searching" I have come across a table of inversions which lists the numbers of inversions $k$ for a number of permutations of lengths $n$ (varying ...
• 11
192 views

### What exactly is the orbit-stabilizer theorem?

Obviously, being a professional group theorist, I know what the orbit-stabilizer theorem is. Or at least I thought I did. I thought that the orbit-stabilizer theorem was that if $G$ is a finite group ...
42 views

### Cyclic permutation with restriction, am i wrong? [closed]

there are 4 boys and 4 girls, how many ways they are arranged to sit in circular table if the 3 boys always together? i found someone's video and the answer is just 5!3!, there are 4 boys why he didn'...
81 views

1 vote
61 views

### How many $n$-digit numbers are there with no or even number of $1$s in them if only digits $1$, $2$, $3$ and $4$ are allowed?

You are given an unlimited supply of each of the digits 1,2,3 or 4. Using only these four digits, you construct n digit numbers. Such n digit numbers will be called LEGITIMATE if it contains the digit ...
• 47
1 vote
I was solving the following problem (1.2.10 from Dixon and Mortimer's Permutation Groups): Given the group $G =\langle(x_1,x_2, x_3, x_4),(x_1,x_3) \rangle$, give an example of a polynomial that's ...
### How many positive integral solutions does $a+b+c+d+e=20$ have, if $a<b<c<d<e$? [closed]
Let $a<b<c<d<e$ be positive integers such that $a+b+c+d+e=20$, then the number of such distinct arrangement possible are __? Please also provide the general solution for every sum of ...