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Mathematics Stack Exchange

Questions tagged [permutations]

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

The word permutation has several possible meanings, based on context. In combinatorics, a permutation is generally taken to be a sequence containing every element from a finite set exactly once. Permutations of a finite set can be thought of as exactly the ways in which the elements of the set can be ordered.

In group theory, a permutation of a (not necessarily finite) set $S$ is a bijection $\sigma : S \to S$. The set of all permutations of $S$ forms a group under composition, called the symmetric group on $S$.

Reference: Permutation.

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How many permutations of pixels in a square?

Given a square of dimensions x by y pixels, how many permutations of colors of pixels are there in the square? Assume that each square is 1 pixel and that this square is 5x5 pixels. How many unique ways can this square of pixels be permuted? Also…
Martin Erlic
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Permutation of Groups - looking for the right term

I'm looking for more detailed information about the following problem, but i'm missing a right keyword, or term for this: Let's assume i have 10 people and they are assigned to groups: person group 0 A 1 A 2 A 3 …
MS1
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Strategies for solving permutations of a word

So I'm trying to prepare for exams, and am having some trouble with permutations, and was wondering what's a good strategy to solve this task is: Given the set of letters $\text{AAABBBBCCDEEFG}$ find: $(*)$ The number of unique permutations of…
Frank Vel
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Arrange numbers to prove question

Prove that 100 0's, 100 1's, 100 2's, 100 3's, 100 4's, 100 5's, 100 6's, 100 7's, 100 8's and 100 9's cannot be used in any form to make a perfect square. I have no idea how to do this question. I was asked this question in a competition. A simple…
Arpit Saxena
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How can it be proven that a cycle of length k is an even permutation if and only if k is odd?

How can it be proven that a cycle of length k is an even permutation if and only if k is odd? I know it can be done using the fact that a permutation which exchanges two elements but leaves the rest unchanged is an odd permutation.
user187039
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repetition of permutations problems bingo

for a game bingo, organizers place one marble with 0 marble on it, one marble with 1, and one marble with 2 and so on up to one marble with 9. Each time a number is called one number is drawn, the digit showing recorded, the marble replaced and…
carry
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Conjugate permutation and "their" $\alpha$

Let $\sigma=(13624)(587)(9)$,$\tau =(15862)(394)(7)$. Determine such $\alpha$ that $\alpha \sigma \alpha^{-1} = \tau $. The elements $\sigma, \tau $ must be conjugate. But how many such $\alpha$ are there? Intuition suggests to me, exactly one.
user180834
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All possible types of permutation.

A permutation $ \sigma \in S_{10} $ satisfies the conditions $$ \forall_{1 \le i \le 29} \sigma^i \neq id, \sigma^{30} = id $$ Determine all possible types of the permutations. Give me a hand.
user180834
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Given $\sigma, \tau \in S_n$, find $\alpha$ such that $\alpha\sigma\alpha^{-1} = \tau$. How many such $\alpha$ are there?

We have $\sigma = (13624)(587)(9)$ and $\tau=(15862)(394)(7)$. Determine a permutation $\alpha$ such that $\alpha\sigma\alpha^{-1} = \tau$. How many such $\alpha$ are there?
user180834
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Letter Arrangement with Permutations

In how many different ways can the letters of the word MAMMAL be rearranged so that the letters M are separated?
Brendan
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Painting parallelopiped with 6 different color

In how many ways can 6 faces of a rectangular parallelopiped with all 3 dimensions distinct , be painted with 6 different colours?? I have tried and i am getting 90 by $\displaystyle\frac{6!}{2^3}$. Thankyou
hiten
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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. For Tens place - It can be filled in 3 ways (from…
rickenjus
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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, the words can be made by $26 . 25. 24. 25. 26$. Is…
Aspiring Mathlete
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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.
sparta93
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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 consecutive occurrence of 'b'. But bbc,abb,bbb have…
Shahed Al Mamun
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