Mathematics Stack Exchange
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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Seating arrangements of four men and three women around a circular table

In how many ways can $4$ men and $3$ women be arranged at a round tale if: i) the women always sit together? ii) the women never sit together? I attempted both the questions but the answers I got don't match the ones given in the source. This is…
GinaJay
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Combination and permutation of indistinguishable objects

There is a group of 10 objects, 2 red, 3 blue and 5 green. The objects are indistinguishable. In how many ways can they be arranged on a line? As there are 3 groups of objects I did that: $ 10! / (2! * 3! * 5!) $ So my result is 25.200 Is that…
jsab
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Number of subset-permutations for a set

Suppose you have a set {a, b, c}. There are 3! = 6 permutations. Subsets {a, b}, {a, c}, and {b, c} will account for 3 * 2! = 6 permutations. Subsets {a}, {b} and {c} accounts for 3 * 1! = 3 permutations. Subset {} accounts for 0! = 1…
Marty
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Number of mixed doubles pairs such that no one plays with his/her spouse?

Can you help me with this problem? There are $7$ married couples. What will be the number of mixed double pairs in tennis such that no one plays with his/her spouse? Can some one help me with this? The answer is $840$. Thanks! EDIT : The…
Egalitarian
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Permutation: How many ways to put 7 people in 10 rooms?

How many ways can 7 people be placed into 10 rooms, if (only) 2 of them can’t share a room with anyone? I'm not sure how to go about this, mostly because of the "share a room" bit. I'm thinking I should calculate the number of ways 2 people can be…
L.Price
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Permutations and disjoint cycles

Write the following permutation as product of disjoint cycles $$(12)(13)(14)(15)$$ Could someone explain how to proceed with this question ? I have four more similar, so I just want somebody to solve this one so that I can have a basic example.…
amir
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The number of words that can be made by permuting the letters of _MATHEMATICS_ is

The number of words that can be made by permuting the letters of MATHEMATICS is $1) 5040$ $2) 11!$ $3) 8!$ $4) 4989600$ First of all I do not understand the statement of the problem, I would like if some one tell me with an example.
Myshkin
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Why does the ordering function invert itself?

I notice in my R console that x=sample(1:n); all(order(order(x)) == x) always evaluates TRUE, for any n. Just to assure you I'm not on the wrong SE site here, I know exactly what the code means, but this still makes my brain hurt. Can anyone draw a…
eric_kernfeld
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Assigning values to permutations

$N$ objects can be arranged in $N!$ different orders. For example, $10$ playing cards can be stacked $10! = 3,628,800$ different ways. Is there a way to assign a numerical value to each permutation so that every integer from $1$ to $N!$ corresponds…
Leroy Nimka
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How many arrangements can be made from the letters of the word "mountains" if all the vowels must form a sting?

I thought we take $4$ vowels and find number of arrangements $4!$ and multiply it with arrangements that can be made with consonants that is $5!/2!$. However my approach seems to be wrong.
R.Temur
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Arrangements using the letters of the word BOOKKEEPER with some constraints

This is my first question here. We are facing difficulty with one permutation question. We were asked to find the different counts possible using the letters of the word BOOKKEEPER. This was easy. The answer can be arrived as 10!/(2!*2!*3!) which…
avantika
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Permutation of 2 or more groups while keeping the ordering of the groups

I've been trying to get a general formula for this, but I couldn't find anything exactly what I need. What I want is, let's say we have 3 groups: (x,y,z),(a,b,c) and (k,l,m) What is the total number of permutations of these three occurring in a…
pdace
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Minimum number of moves (not swaps) to transform one permutation into another

I have an initial permutation (eg. $\{A,B,C,D,E,F,G,H~\}$) and a final permutation (eg. $\{A,C,F,D,E,G,B,H~\}$) and I want to find how the final permutation can be created from the initial one using minimum number of moves. In my situation a move is…
Matej Vargovčík
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Minimum Number of Races to win the Formula 1 World Championship

There are a few complications in the allocation of Formula 1 points through the season, such as half points for an incomplete race, and the fact that a team can change drivers mid-way through a season. However, if we assume the same 20 drivers all…
Party Ark
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How to find a permutation of a specific rank?

I have a problem regarding permutations. When the rank of an unknown $S_7$ permutation is given, I want to find this permutation, but I can not. For example, I have the following questions: Find the $S_7$ permutation which has I) rank(1000) II)…
Jimbo_ai
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