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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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Ordered selections problem - restaurant problem.

Question: A restaurant has five entrees, seven main courses, and ten desserts. In how many ways can you select two dishes on the condition that they must not both be from the same part of the menu? The answer is 155. I have no idea what qualifies as…
Dom Turner
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What is the total permutation equation with a set of distinct permutation combinations?

I am working on a game where there is always 4 opponents. Each opponent is one of 4 classes and there is always 1 of each class. I want to know how many permutations are possible given an equal distribution of units per class. For example. If I had…
Aggressor
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How to find the number of derangements by only considering the first 'k' indices?

Method to calculate the number of derangements for any given 'n'(length of permutation) : https://en.wikipedia.org/wiki/Derangement Suppose, for n = 3, the derangements are as follows : - 1 : {3,1,2} 2 : {2,3,1} (Meaning of derangement : All…
Shalini Tomar
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How can I prove that the sign of the permutation below is $(-1)^n$?

How can I prove that the sign of the permutation below is $(-1)^n$ $k↦n+1−k$ (A permutation with reflection property). I tried using induction but it did not help ( For $n=1$ I get that the sign is $1$ (even permutation) but $(-1)^1=-1$ Thank you…
FAF
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How many ways can five girls and five guys stand in a line

this is a question that I am struggling with. I thought I did it correctly, but the answer key used a different method. The question: "How many ways can 5 boys and 5 girls stand in a line if the girls and boys alternate throughout the line?" The way…
Nicole K
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Counting in a rectangular grid with obstacles

Rectangular grid of given dimension I was asked to find the no. of ways to get from (0,0) to (8,8) with the 4 points of the shaded box unpassable, aka I can't use the 4 points namely (3,3)(4,4)(3,4)(4,3) while on my way to (8,8). Right and up…
bearbearsocute
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Determining Permutation/Combinations with Bit Strings

I've got a discrete math problem on my hands...I'm trying to understand the steps behind working with bit strings; specifically, how a bit string of x length has "at least" or "exactly" a certain number of ones or zeros. I understand that it likely…
Emily
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Does every permutation, which is not an $n$-cycle, commute with some transposition?

This question addresses how many permutations $σ∈S_n$ commute with a given transposition $(i \space j)$. What about the other way around, namely: How many transpositions $(i \space j)$ commute with a given permutation $σ∈S_n$? I know that if…
user750041
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How many ways to give five different books to three students?

How many ways to give five different books to three students? A student can have all of them. My attempt 1) Three ways to give separately five each (5,0,0) - 3 ways 2) 4 gifts for one and one gift for another - $^5C_4\times3\times2$ 3) 3,1,1 -…
Angelo Mark
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Permutations at most x duplicates in article

Let's say we have 50 numbers (1 - 50). Each data set contains 5 numbers. How many sets are there, where there are at most x duplicates between two sets. No duplicates within a set are allowed. Example with less data; Let's say we have 10…
Rick
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Finding the number of fleets formed form a certain group of ships

An army fleet is made with 4 cargo ships, 6 cruisers, 3 battleships, 7 destroyers and 3 aircraft carriers. The army has 7 cargo ships, 7 cruisers, 8 battleships, 10 destroyers and 5 aircraft carriers. How many different fleets can be made? The way I…
RishtarCode47
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Question related to combinations, counting and listing

Assume that you are to generate computer password codes using 10 consonants and 5 vowels. How many different passwords can be generated if each password is made up of 3 consonants and 2 vowels?
Rogan Nithin
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Explanation of the 'division of $52$ cards' in four groups of $13$ problem?

I have been thinking about this problem, total possible combinations of division of $52$ cards deck in $4$ groups of $13$. I remember that the answer was ${52 \choose 13 }{39 \choose 13} {26 \choose 13} {13 \choose 13}$ What I want to know if figure…
Max
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Confusing combination-permutations question

In a shop there are five types of ice-creams available. A child buys six ice-creams. Is it true that the number of different ways the child can buy six ice creams is equal to the number of different ways of arranging 6 A's and 4 B's in a…
syfluqs
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Simple permutations for all $k$

a)How many are the simple permutations of the numbers $ 1,2, ..., n $ in which the k-th element is less than $ k + 4 $, for every $ k $? b)How many are the simple permutations of the numbers $ 1,2, ..., n $ where the kth element is greater than $…
Lambert macuse
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