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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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Do Permutations allow for repeats if not specified

Given the following question, quoted verbatim: How many permutations of all the letters $ABCDEFGH$ contain the strings $CAB$ and $FAD$? Would the answer be $0$? Because the way I understand it, permutations of a set of distinct items by…
user3776749
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There are 13 apples, 2 pen, divided to four children(A,B,C,D) Everyone has at least one thing Q:How many method?

There are 13 apples, 2 pen, divided to four children(A,B,C,D) Everyone has at least one thing Q:How many method ?
user387513
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Possible ways of distributing?

What is the possible ways of distributing 10 identical things among 6 children My solution is "out of 10 identical things 6 can be given to 6 children in only one way,since the things are identical,Now the remaining 4 identical things can be…
Neeraj Sharma
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Number of microstates in a two level system

This sounds like a physics question but I'm sure of all the physics aspects. I'm going wrong somewhere though, in the maths. At high temperatures, the occupancy of energy levels becomes equal, so in this case both levels will have $\frac{N}{2}$…
user13948
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Find the numbers between $1500$ and $5000$ that can be made from the digits $1,2,4,5,7$ and $8$ if each digit is only used once.

Find the numbers between $1500$ and $5000$ that can be made from the digits $1,2,4,5,7$ and $8$ if each digit is only used once. Can someone show the steps?
Heng Yong Wei
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How to find all the elements of the group $S_4$

I know how to find all the elements up till $S_3$ but for $S_4$ I am not sure how to do that systematically.
krishneel
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Arrangement of the word DIAGONISE such that each word start with a vowel and ends with a consonant

How many arrangements can be made using all the letters of the word DIAGONISE such that each of these starts with a vowel and ends with a consonant?
Kme
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Permutions that commute

So I have two permutations for which i worked out the product disjoint cycles. f = (1 2 4)(3)(5) and h = (1)(2 4)(3)(5), i also worked out the order of both, but how can you show that they commute if they do at all. I know this is basic, Im just a…
MooeSha123
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How many $n$ digit numbers formed from $n$ digits where a digit can be repeated twice?

So I had a problem saying how many $3$ digit numbers can be formed from the numbers $\{1,2,3\}$ where a digit can be repeated twice and the written answer was $18$. When I tried to solve it myself by tree diagram and counting it was $24$ numbers.…
maged rifaat
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Permutation , specific distance between elements

In how many ways we can rearrange 2 people A and B where their distance is at least 4 seats apart from each other in 8 seats? I tried to follow the round table permutation problem but I got lost because I know that there are 10 possible places where…
Kurama
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permutation count for a k-length word in a language

Given an alphabet of A different letters, how many K length words can we form that have exactly D different letters? The answer is given here: Permutations of fixed length words of an arbitrary alphabet with fixed number of different letters but,…
davidS
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Permutations given n = 12, r =5

Given: a team of 5 is made up of 12 students. which means n = 12, r = 5. Find: 1.) # of possible teams. 2.) # of possible teams when 2 students won't play together. 3.) # of possible teams when 2 students MUST play together. My attempt: 1.) nCr = 12…
OrangePineapple
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Proof involving permutations

Let $\delta = \begin{pmatrix} 1 & 2 & 3 & 4 & 5\\ 2 & 3 & 4 & 5 & 1 \end{pmatrix} \in S_5$ be a permutation. If $\tau \in S_5$ has the property that $\tau \delta^2 = \delta^2 \tau$, prove that $\tau \delta = \delta \tau$. I've tried to multiply…
George R.
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Circular permutations in a particular order

I just need these checked. The symmetry in circular permutations is a bit confusing. What is the probability that 6 people sit in a circle in alphabetical order? How many ways can 6 people sit in a circle? Two arrangements are the same if you can…
user369210
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Permutation with repetitions / non-distinguishable objects basics

The question was: From the letters in MAGOOSH, we are going to make three-letter "words." Any set of three letters counts as a word, and different arrangements of the same three letters (such as "MAG" and "AGM") count as different words. How…
neonant
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