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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What exactly are $\rho_i, \rho_j$ and what is their role in the cyclic factorization?

I'm reading Beardon's, Algebra and Geometry. Here: I'm having a little trouble understanding the marked part. In the expression $\rho_j(x)=\rho(x)$, who is $\rho_j(x)$? Is it one cycle that is equal to the entire permutation? And in…
Red Banana
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permutations for people in a circle

in how many ways can 20 members sit in a round Boardroom if the chairman must sit between the secretary and the treasure?i tried (20-1)!3!*2 but the answer seems to be alittle exaggerated.help me
Rapper Ace Morris
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24 Children, 6 types of candy, 4 of each candy. How many ways are there to give all the children one candy?

Let's say you have 24 children, and 6 different flavours of candy, which 4 of each flavour. A child cannot get more than one candy. How many ways are there to distribute these 6 flavours of candy? Edit: The solution For the first flavor, 4 of the 24…
gsamerica
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Number of ways to write 5 digit number with restriction?

How many ways to write a 5 digit number so that every digit is scritctly greater than the digit on it's right ? How could we derive a formula for such a N digit number where N <= 9 ?
Bharat Kul Ratan
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Permutations of not selecting the right size of dress for 3 daughters

I am trying to solve the following problem and the answer I am getting is (6 - 1) = 5 but the answer is given as 2. Problem A father purchased dress for his 3 daughters. The dresses are of same color but different size and they are kept in dark…
Sunil
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Permutation equation. How to solve an equation when having a big exponent

$\sigma =\bigg(\begin{matrix} 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11 \\ 3 & 4 & 5 & 7 & 9 & 2 & 8 & 6 & 1 & 11 & 10 \end{matrix}\bigg) \in S_{11}$ Find $ \tau \in S_{11} $ for which: $\tau^{2011}=\sigma$ I do really have no idea on how to do…
ITChristian
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Permutation logic is missing something

I am trying to solve the following question and my logic seems correct but my answer is not matching. "In how many ways can letters of the word $\text{CALENDAR}$ be arranged so $\text{C}$ and $\text{A}$ are together as well as $\text{N}$ and…
Sunil
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How many ways are there to arrange letters of the word GARDEN with vowels in alphabetical order?

The solution says that half of the total number of arrangements would have A before E . How is that?
Sidd
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How to express the condition in permutation formula.

I have a very basic and conceptual doubt regarding the function of the permutation formula. I am going to ask them through some examples in which I applied them and could not proceed. The first basic thing is that let us say I have four dice and I…
Harsh Sharma
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How do I calculate the number of permutations of a specific binary string?

For a binary string of 6 elements with three ones and three zeros in each string, how do I calculate the total number of string permutations? For example, 3 possible strings would be 100011, 111000 and 101010.
Mel
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Permutations and Combinations in arranging letters

Number of ways to arrange the letters $(A,A,A,A,A,B,B,B,C,C,C,D,E,E,F)$ such that no two $C's$ are together ? My solution: I calculated all possibilities with CC together i.e $\dfrac{14!}{5!3!2!}$ and subtracted it from total i.e…
Rakshit Jha
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Finding order of permutations

Consider the following disjoint cycles: (1 3 2)(6 4) (7 5 9 8) I'm aware that to find the order of a permutation we take the lcm. However, here we have three disjoint cycles. So do we first take the lcm of the first two: lcm (3, 2) = 6, and then the…
user384316
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Permutations and Combinations with Divisibility.

If sum of digits of a 7 digit no. is 59, In how many ways can this number be divisible by 11? For divisibility by 11 the difference of the sum of digits at even position and the sum of digits at odd positions should be divisible by 11. I can't…
Rakshit Jha
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number of ways of selecting $ n$ things from $3n$ things

What are the number of ways of selecting $n$ things out of $3n$ things out of which $n$ are of one kind and $n$ are are second type and rest are unlike ?
a25bedc5-3d09-41b8-82fb-ea6c353d75ae
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Permutation word problem

A box has 7 green items and 5 black items. We randomly pick 2 items from the box. What are the odds that both items are green if we know that the first item is green?
user394807
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