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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what is the formula to calculate the permutations

I am new to the permutations. I have a problem with me for which I am not able to use proper formula - Problem: There are X boxes in which balls need to be placed. The balls are of two colors - BLUE RED. We have unlimited balls of both colors. We…
ANKIT
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How to find a permutation $\sigma$ given the permutation $\sigma^2$?

How to solve the equation: $\sigma ^2 =\left({\begin{array}{*{20}c}1 & 2 & 3 & 4 & 5\\ 1 & 4 & 2 & 3 & 5\end{array}}\right)\ $ where $\sigma \in S_5$. Is there a general method?
sprave
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Permutation for balls

Possible Duplicate: number of combination in which no two red balls are adjacent. We have $N$ slots. They have to be filled with balls (either green or red), one ball for each slot. Green balls can not be placed in consecutive slots. Find the…
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How many words can be formed using all the letters of "DAUGHTER" so that vowels always come together?

How many words can be formed using all the letters of "DAUGHTER" so that vowels always come together? I understood that there are 6 letters if we consider "AUE" as a single letter and answer would be 6!. Again for AUE it is 3!, but I didn't get why…
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Permutation of Indistinguishable Objects

How many number of two digit numbers can be formed using $\{4,5,6,6\}$ without repetition? I know that $\{45,46,54,56,65,64,66\}$ are the possible answers, but I am wondering if there is any formula that can be used to get this. I tried this formula…
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Rewrite permuatation as disjoint cycles

Rewrite $(3412)(245) \in S_4$ as a product of distinct cycles. I've only ever been given permutations as distinct cycles, transpositions or the matrix notation so I have no idea where to start.
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Number of ways to place 4 girls into 3 bedrooms.

A family has 4 girls and 3 bedrooms. 2 of the bedrooms are only big enough 1 girl, and the last room is big enough for 2 girls. How many ways are there to assign the girls to the bedrooms? I came up with 4!/2! I thought that because there are 4…
Tyler
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6 dogs and 4 cats enter a race, in how many ways can a dog finish first, second and third?

If using permutations 6*5*4 would give 120 ways that that dogs could occupy the first, second and third place. Is that correct?
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Permutation of order 12 and 30 in $S_{9}$

If I have the group $S_{9}$ and $\sigma, \tau \in S_{9}$ where $\vert \sigma \vert = 5$ and $\vert \tau \vert = 6$ is it then possible to have $\vert \sigma \tau \vert = 30$ and $\vert \sigma \tau \vert = 12$ why/why not?
bemyguest
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Prove that $L_7$ is a subgroup of $S_7$

Let $\sigma(v)$ denote the signature of the permutation $v$. Is the subset $L_7 = \{v\in S_7 : \sigma(v)=-1\}$ a subgroup of $S_7$? I am not sure I am proving it the right way. To prove that $L_7$ is a subgroup first I have to show that for any…
KeykoYume
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Number of possible 4 digits number

I was solving a question paper and i stuck due to some missing concepts. please help me out.I want the shortcut to solve this type of question too. Question:Find the number of all four digit numbers whichare greater than 2367 and in which the digit…
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Arrangement of the word MATHEMATICS if last spot must have the letter 'T'

How many ways can the word MATHEMATICS be arranged if the last letter must be a T? My solution: There are $2$ possible choices for the last letter (There are $2$ different T's), which leaves $10$ choices for other places. However, the letters 'M'…
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Permuations and Combinations problem

A football team consists of 3 players who play in a defence position, 3 players who play in a midfield position and 5 players who play in a forward position.Three players are chosen to collect a gold medal for the team.Find in how many ways this can…
Irtiza
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finding number of triangles inscribed in a circle

How to find the number of acute angle and obtuse angled triangles that can be inscribed in a circle containing 'N' equally spaced points.
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What did I do wrong in the permutations question.

I was given the following question: A hardware store sells numerals for house numbers. It has large quantities of the numerals 3, 5, and 8 but no other numerals. How many different house numbers, with no more than three digits can be made from these…
anonymous
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