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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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Permutation of Automobile License

How many different automobile license numbers can be formed by using $1$ to $6$ digits preceded by a letter if the digit immediately following the letter cannot be zero and the letters O and I are excluded? My answer…
Madisson
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application of permutation in arranging numbers

How many numbers can be formed with the digits 3,4,5,6,7 which are greater than 1000(repetition is not allowed) ?i think 2 parts will be there.first from 1000 to 9999.next from 10000 and above.i could not get the correct answer
Harsh Vardhan
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Set of Permutation and Identity Permutation

I have a "basic" math question that seems easy but I couldn't figure out. Assume I have $L$ = {0,1,2,3,4,5,6,7,8,9} and $M$ = set of all permutations on set $L$. From the description above, I know that the $|L|$ = 10 and $|M|$ = 10! Now let $J$ =…
ThomasWest
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Problem on a permutation and its cyclic decomposition

Let $n \geq 4$ be an even integer and let $S= \{1,2,\ldots,n\}$. Fix an element $r \in \{1,2,\ldots, \frac{n}{2}-1\}$. Define a map $f: S \longrightarrow S$ by $f(t)=s$, for all $t \in S$, where $s$ is the remainder when $t+r$ is divided by $n$.…
RKR
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Alphabet Permutation Problem

Find the number of words of length $8$ of distinct letters of the alphabet so that the words do not have both $A$ and $B$ in them. I know the answer is $P(26,8) - (8)(7)(P(24,6))$, but I don't understand why completely. Why do I need to multiply…
NikNik
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need good permutation function to scramble sequential numbers to hide total amount and prevent guessing

I have about 70,000 items in a database. I want to serve these items to the public with an id which is currently in sequential order (1, 2, 3, 4 ....). I don't want someone with a bot to just look up requests in the obvious order. I want to scramble…
Cit5
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In how many different ways can you put 3 balls into 5 boxes, when having more balls in a single box is also allowed?

before anyone starts blaming me for stating something incorrectly, I copied down the question from my book word by word so I am sorry. I don't know how to approach the problem please help. I was thinking of dividing 3! by 5! but that does not make…
user443248
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Inducing a Permutation

I'm trying to understand the following, from the OEIS, sequence A294673: a(n) is equal to the order of multiplication-by-2 acting on the set of non-zero elements in (Z/(4n+3)Z), modulo the action of +-1. To be precise, identify i=1,2,...,2*n+1…
user156506
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defining even and odd permutations in terms of smaller value following larger

I read the definition of an even permutation on wiki to be the number of elements of the original sequence had to be exchanged to get the new sequence. By that definition if we start with (1,2,3) then 1,3,2 is an odd permutation because we just…
MHall
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People to re-arrange so that neighbors changed

In how many ways 20 people be re arrange so that everyone had a different right hand neighbour in new arrangement
Pankaj
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Counting semi-ordered permutations

We call a permutation $\sigma$ of $\{1,2,...,n\}$ a semi-ordered permutation if $\sigma_1 > \sigma_2 > ... > \sigma_{k-1} > \sigma_k < \sigma_{k+1} < ... < \sigma_{n-1} < \sigma_{n}$ where $\sigma_i$ is the number placed at position $i$ of the…
TheNotMe
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How can i solve this permutation (idk if its permutation tho) problem?

Six students in a math class all have to present their homework to their teacher, one student insists on being the first one to present. If the student's request is granted how many ways are there to schedule the presentation? I tried $1 \times 5! =…
user503579
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Misunderstanding basic permutations

I am currently misunderstanding a very basic section of a paper I am reading. An extract follows: With $\mathcal{L} = \{v_1 = mild, v_2 = severe, v_3 = very~mild, v_4 = very~severe\}$. In this case, there is a permutation $\sigma$ of $1,\ldots…
Astrid
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Can a permutation of 9 elements with order 4 have no fixed points?

My thinking is With 9 elements, having order 4 means either a single orbit of length 4 and zero, one, or two orbits of length 2; or two orbits of length 4. in both cases, the number of fixed points (not in one of the orbits) is odd, so can't be…
laugh salutes Monica C
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Prove that we can express any permutation as a product of permutations of the form $(12)(13)...(1n)$

I know that any permutation can be written as a product of transpositions. Does that complete the proof? I don't think so, because suppose we need $2\rightarrow 3$, we can't write that in the form $(1n)$.
user425169
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