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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Coloring vertices of a square

Using four colors, red, white, blue and green, in how many ways can the vertices of a square be colored? Assume that reflections and rotations are allowed, meaning that if you examine a square from front or back it represents the same coloring, and…
user71998
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arrangement of balls in bowls

There are five bowls numbered $1$ to $5$. There are $5$ green balls and $6$ black balls. Each bowl is to be filled by either a green or black ball and no two adjacent bowls can be filled by green balls. If the same color balls are indistinguishable,…
vickyace
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Difference between permutations

Given the following: 1) Is it wrong to say (1 2 4) (5 3) = (1 2 4) (5 3) or = (3 5) (1 2 3) ? 2) What is meant by ( 1 2 3 4 5 ) and 1 2 3 4 5 ? And why are they not equal? Thanks!
user138913
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Permutation Multiplication (easy)

Given α◦β=(1532)(14)(35) How do we get from the given to = ( 1 4 5 2 ) ( 3 ) = ( 1 4 5 2 ) = (4 1 3 5 2) ? Thanks
user138913
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How many different ice cream cones with 31 different flavors and 2 kinds of cones?

I have been trying this for a while now. Using the formula for permutations, I am getting P(31, 2) = 10,230, but this seems way too high... An ice cream shop has 31 different flavors of ice cream and two kinds of cones. The rules are, cones can be…
MathApprentice
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Mapping permutations to an index

I'm trying to calculate the distance-table (#of states as a function of the distance) of the 15-puzzle (has been done before in 2005 on a supercomputer by Korf et al.). There are $16!$ different states, or nodes, in the tree that needs to be…
JorenHeit
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Permuting "123456728905"

In how many ways can 123456728905be permuted such that, neither two 2's nor two 5's are adjacent to each other ? I'm really confused how to ensure those conditions? 0 is allowed to come as the first. Consider these are simple characters, not as a…
vaidy_mit
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Word combinations Bamboozled?

I have a list of 1,626 random words. How can I work out the total number of combinations abiding to a limit of 12 words per thing ? E.g dog fish cat whale shark snake spider eagle nine dog clam ray dog fish cat whale shark snake spider eagle nine…
mattyboo
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$11$ matches are to be played,Each having $3$ distinct outcome,

$11$ matches are to be played,Each having $3$ distinct outcome, in how many ways one can predict the outcomes such that $6$ outcomes turn out to be correct? My thought $11C_{6}\times 3^5$ am I right?
Myshkin
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How many $n$ digit numbers can be written using only certain digits?

For example, how would I calculate how many $5$ digit numbers I can write using only digits $0, 2, 2, 3, 3$? Is $4\times5\times5\times5\times5$ correct or am I missing something?
Tool
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how can I show that the sum is equal to one,considering the number of permutations that move exactly k elements

Knowing that $a_{n,k}=\binom{n}{k}D_{k}$ ,where $D_{k}=\left |\left \{ \sigma \epsilon S_{n}:\sigma(i)\neq i, \forall i=1,...,n \right \} \right |$ and $a_{n,k}$=the number of permutations that move exactly k elements, how can I show that:…
evinda
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number of ways of forming a digit

We have been given six digits 0,1,2,3,4,5. Now what is the no. of ways in which these six digits can be used to form a three digit number divisible by 3 provided that the repetition of digits is not allowed? I am fully aware that any number which is…
Avery
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possible outcomes when dice are thrown?

What are the possible outcomes when a 'm' sided die is thrown 'n' times? and What are the possible outcomes when 'n' dice are thrown at a time having 'm' sides each?
praneeth
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A group having prime order such that any normal subgroup of which lies in Z(G).

show that in a group G of order p^2 any normal subgroup of order p must lie in the center of G.
user110666
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Multiplying Cycle Permuations

I am having trouble multiplying permutations in cycle notation. (1 3 4 5) (2 3 4) = (1 3 5) (2 4) I do not understand how this product is determined. My answer is (1 3 4) (2 5). I have come to this conclusion by switching the order to (2 3 4) (1 3 4…
user98643
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