# Tagged Questions

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

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### Permutation & Combinations - Distribution

The number of ways in which n distinct things can be distributed among n people so that at least one person does not get anything is 232. Find n. I think every object has (n-1) option. So (n-1)^n=232. ...
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### Find the number of ways this can be arranged in which no 2 women and no 2 men sit together given 4 men and 3 women are seated in a dinner table?

Find the number of ways this can be arranged in which no 2 women and no 2 men sit together given 4 men and 3 women are seated in a dinner table? @Edit: They are seating in a row dinner table I have ...
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### Why does $\operatorname{SL}_2(3)$ only yield even permutations?

$\newcommand{\pa}[1]{\left(#1\right)} \newcommand{\pamat}[1]{\left(\begin{array}{cc} #1 \end{array}\right)}$ In an exercise lesson for Algebra 3, we were proven that the special linear groups over ...
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### Probability of Boys and Girls in Row

Ten male friends and six female friends line up next to the bus stop in a row. Everyone just positions themselves at random. What is the probability that no two females are sitting next to each other? ...
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### Rearrangements that never change the value of a sum

Which bijections $f:\{1,2,3,\ldots\}\to\{1,2,3,\ldots\}$ have the property that for every sequence $\{a_n\}_{n=1}^\infty$,  \lim_{n\to\infty} \sum_{k=1}^n a_k = \lim_{n\to\infty} \sum_{k=1}^n a_{f(k)...
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### $S_6$ contains two subgroups that are isomorphic to $S_5$ but are not conjugate to each other

This is a problem from Ph.D. Qualifying Exams. Show that the symmetric group $S_6$ contains two subgroups that are isomorphic to $S_5$ but are not conjugate to each other. Here is my method. $S_5$ ...
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### Conjugation of permutation group $S_n$

I want to find the conjugacy classes of the permutation group $S_n$ To start with I think I have to prove that $\pi(\sigma_1\dots \sigma_m)\pi^{-1} = (\pi(\sigma_1)\dots \pi(\sigma_m))$. Where $\pi$ ...
### 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 ...
if I have $n$ drawers and in each drawer I can only have 1 pen or 1 pencil for example if i have $3$ drawers the possible ...