# Tagged Questions

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

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### Number of shoes to be taken out.

There are $7$ pairs of black shoes and $5$ pairs of white shoes. They are all put into a box and shoes are drawn one at a time. To ensure that at least one pair of black shoes are taken out, ...
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### Combination of N-number list with M enabled items

I have a list of N numbers (boolean), where a exactly M of them must be selected (true), not more or less. An item of the list can only be selected (1) or not selected (0). Example with N=4, M=3: [...
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### Find all permutations of length n from a set of m values

If I have a set of values, say, [0, 1, 2, 3, 4], how can I find all permutations of a given length (that is less than the number of values in the set)? For example, how would I go about finding all ...
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### Number of orderings with tree-based constraints

How can I compute the number of possible orderings of the numbers $1,\dots,N$, where some constraints are given on the relative order of some numbers? I know how to do the calculation in simple cases....
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### The wreath product $K ~\mbox{wr}_{\Gamma} ~ H$ acts faithful on $\Delta \times \Gamma$ iff $K$ acts faithful on $\Delta$

Let $K$ and $H$ be groups, and let $H$ act on $\Gamma$. Also let $\operatorname{Fun}(\Gamma, K) = \{ f : f : \Gamma \to K \}$ be the set of all functions from $\Gamma$ to $K$. This set is a group ...
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### 6-team Round Robin

Is it possible to create a schedule where we have 6 teams play 5 different games with each team playing each game and each team only once? Or do we have to increase the amount of games to make this ...
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### find coordinates are of a parallelogram

if the coordinates are (1, 2) (4, 3) (1, 0) (-2, -1), how can we can find whether it is of a parallelogram or not
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### 16 teams enter a competition

16 teams enter a competition. They are divided into four pools (A, B, C and D) of four teams each. Every team plays one match against the other teams in its pool. After the pool matches are completed:...
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### In how many ways can a group of 5 boys and 5 girls be seated in a row of 10 seats?

In how many ways can a group of 5 boys and 5 girls be seated in a row of 10 seats? Still having some confusion with the difference between combinations and permutations. I have tried this problem ...
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### Better explanation of conjugation of permutations?

It says here that $\rho = \tau \sigma \tau^{-1}$, and if $\sigma(i) = j$, then $\rho(\tau(i)) = \tau(j)$. So take for example $\sigma = (1 3 2 4) (5 6)$ and $\rho = (5 2 3 1)(6 4)$. To find $\tau$, it ...
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### A restaurant offers 5 choices of appetizer, 10 choices of main meal and 4 choices of dessert.

A customer can choose to eat just one course, or two different courses, or all three courses. Assuming all choices are available, how many different possible meals does the restaurant offer? So here ...
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### Permutations of sets within larger sets

I am trying to find a formula to give me the number of permutations of 3 numbers across multiple sets of numbers. For example I have 5 different sets call them a,b,c,d,e with numbers 1-10 and I want ...
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### $4$ digit numbers divisible by $5$ formed with $0,1,2,3,4,5,6,6$

How many $4$ digit number divisible by $5$ can be formed with the digits $0,1,2,3,4,5,6$ and $6$? $a.)\ 220\\ \color{green}{b.)\ 249}\\ c.)\ 432\\ d.)\ 288$ I tried Case $1$. $\text{ _ _ _ 0}$...
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### Permutation with repetition and condition

Given an integer $N$, Find how many strings of length $N$ are possible, consisting only of characters A, B, C with each character occuring at least once. Solution: Lets place A,B,C (at least once) ...
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### The total number of games played in chess tournament

There are two women participating in a chess tournament. Every participant played two games with the other participants. The number of games that the men played between themselves proved to ...
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### A primitive permutation group with abelian point stabilizars

Suppose that $G$ is a group acting primitively on a set $X$. Also suppose that all of its point stabilizers are abelian. I want to prove that $G$ is either regular of prime degree or a Frobenius ...
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There are three cities $a,b,c$. Each of these cities is connected with the other two cities by at least one direct road. If a traveler wants to go from one city to another city, she can do so ...
### How many ways are there to split $n$ students into groups of size $x$ OR $y$ ($50$ students into groups of $5$ or $6$)?
How many ways are there to split $n$ students into groups of size $x$ OR $y$ ($50$ students into groups of $5$ or $6$)? I understand there might not be an equation in general but is there an ...