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.

12854 questions
2
votes
2 answers

total number of sequence of digits 9 with digits from set [0,1,2]

question is find total number of sequence of digits $9$ with digits from set $[0,1,2]$ which either begins or end with $210$ digits begin with 210 are $3^6$ digit end with $210$ are $3^6$ in both cases there is extra counting of same nunbers likw…
Gathdi
  • 1,402
2
votes
1 answer

Number of permutations of a set which contains 55 elements

I am to find the number of permutations of a set which contains $55$ elements and the permutations meet following requirements: $$\forall_{i\in \{1, 2, ..., 55\}} f(i)\neq i \wedge f \circ f = id$$
Hendrra
  • 2,868
  • 1
  • 18
  • 35
2
votes
1 answer

Permutations with restrictions on item positions

We are given a set of distinct objects, e.g. $\{a,b,c\}$, and each object can be assigned to a mix of different positions, e.g. $a$ can be in position $1,2$ $b$ can be in position $1,2,3$ $c$ can be in position $2,3$ Is their a formulaic way to…
Bodmas12
  • 41
2
votes
1 answer

Rearranging Equations with Factorials?

Hullo! This is my first time using this site. I have just begun tutoring a Math 12 student and I'm a little rusty on factorials. The stuff I'm stuck on is why : n!/(n-2)! = n(n-1). I seem to be able to come up with the solutions to the following…
Andy
  • 117
  • 2
  • 5
2
votes
2 answers

In how many ways 5 boys and 3 girls can be seated such that no two girls are together?

In how many ways $5$ boys and $3$ girls can be seated such that no two girls are together? Now I came up with a arrangement as GBGBGBBB Clearly, the boys can sit in $5!$ ways, but I am having a bit of trouble with girls as the third girl (prior to…
J. Deff
  • 1,588
2
votes
2 answers

Letters are arranged in boxes

Ways =(selecting one box from upper and lower rows)(selecting four boxes out of remaining)(number of ways arranging six letters in these boxes) $$={3\choose 1}{3\choose 1}{6 \choose 4}\cdot6!$$
a25bedc5-3d09-41b8-82fb-ea6c353d75ae
  • 1,769
2
votes
3 answers

Is it possible to have Stars and Bars Representation of 3 unique type elements?

Given, that we have the 5 letters a, a, b, b, c Now we need to arrange them in such ways where 2 identical letters are not placed side by side. How many permutations of such condition can we have? My question is that, how can I represent this…
Rangan Aryan
  • 399
2
votes
2 answers

Permutations when some objects are alike

I am trying to find the total number of signals that can be created from $3$ pink, $3$ white and $2$ black flags when arranged in a straight line. But, only $5$ flags are allowed in a signal. I know how to find permutations in this situation when…
Sunil
  • 195
2
votes
1 answer

Permutation identities similar to $(7901234568 / 9876543210) \cdot 1234567890 = 0987654312$

It is well known that $9876543210/1234567890 = 109739369/13717421 = 8.0000000729...$ (See for example) Recently I posted at http://list.seqfan.eu/pipermail/seqfan/2012-October/010235.html my observation that exactly the same ratio also could be…
Alex
  • 56
2
votes
0 answers

Let $S_4$ be the set of all permutations on $4$ symbols

Let $S_4$ be the set of all permutations on $4$ symbols and $A$ a subset of $S_4$ such that $$A = \{f\in S_4 : f \text{ is a 3-cycle}\},$$ then $|A|= \mathord{?}$ (included from comments) I think number of $3$-cycles of $S_4$ is ${}^4C_3 \times…
Halima.Khatun
  • 807
2
votes
2 answers

Difference Between Permutations Divisible by 9?

Given a permutation, for example: 1234 1243 . . 4321 Can anybody explain why the differences between numbers are always (no proof, but for all simple permutations) divisible by 9?
PaulQ
  • 23
2
votes
1 answer

Permutations and combinations two part question

This is for some personal combinations / permutations study, I was wondering about a certain type of question that I shall phrase thus: Given 17 of object A and 13 of object B, how many ways may four A objects and three B objects be ordered in a…
Kryptonite
  • 23
2
votes
1 answer

Limit of probability that a permutation of $\mathcal{S}_n$ has a $k$-cycle is $1 - e^{-1/k}$?

Choose a random permutation $\sigma \in \mathcal{S}_n$. What's the probability that it contains a $k$-cycle as you take $n \to \infty$? I ran a couple examples and it seems to approach $1 - e^{-1/k}$. Can anyone explain this phenomenon?
MT_
  • 19,603
  • 9
  • 40
  • 81
2
votes
0 answers

Do permutations apply to places or indices?

Do permutations such as those in the group $S_3$ move elements based on place (of elements in the input) or index? E.g. does $$\bigg(\frac{123}{231}\bigg)$$ move 1 to 2's place (e.g. if the input is 132, then the above permutation would result in…
mavavilj
  • 7,270
2
votes
1 answer

distribution of 101 coins to three friends

In how many ways we can distribute 101 coins to three friends such that sum of the coins of two friends is more than or equal to the number of coins of third friend. my views:should I distribute 50 and then 51 ,52 coins ....is there any elegant way…
user344005
  • 85
1 2 3
…
69 70