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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How to express "$k$ things are the same" and "$n-k$ differ from each other as well as the $k$" as number of permutations?

How to express "$k$ things are the same" and "$n-k$ differ from each other as well as the $k$" as number of permutations? I start with the obvious, which is the $n-k$ things differing from each other, which gives $(n-k)!$ permutations on the set…
mavavilj
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Calculating permutations that has no 2 repeated members

I'm trying to figure out a way to calculate this permutation (as an example): size n = 5 members = {0, 1} On this case we have 2^5 possibility to form a group of 5 numbers using 0 and 1 (e.g. 00000, 00001, ...) The question is, how can I subtract…
Heidar
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Permutations: How many outcomes have a 1 in them if P(n,k) = P(13,3) and the probability it will occur if randomly generated?

There is a set of numbers {1,2,3,4,5,6,7,8,9,10,11,12,13}. I am trying to find out how many subsets I can form that have 3 numbers in them and also the amount of subsets that will have a number 1 in them. Also, if I was to randomly generate a single…
Lobster
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permutation-8 people forming a circle with two to be seated with each other

I have one last question regarding permutation. I understand the problem and the rule of product but this problem seems to be in a different format compared with the two questions I asked before. A committee of eight is to form a round table…
Leonzo Escolar
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Permutations Properties: transpositions

Let $\tau_{ij}$ be a transposition if degree n. What does it mean when one says that $\tau_{ij}=\tau_{ji}$? Thanks in advance!
Anonymus
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Number of ways to distribute balls in three different boxes.

The number of ways to distribute 5 red,6 black and 7 green balls equally in three different boxes such that all the boxes get balls of all the three colours. (assume balls of same colour are identical) My attempt: Assume the three boxes get $x_1$,…
user8167818
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Permutation Notations

In a permutation consisting of numbers {1, 2, 3} What's the difference between the permutation notations $(x_1, x_2, x_3)$ where it's a specific/particular permutation and $(X_1, X_2, X_3)$ where it's a random permutation. $(x_1, x_2, x_3)$ could be…
A_for_ Abacus
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Number of ways to arrange 4 digits such that there is at least one same pair

For example Not Accepted values: $4444$ (4444 is not a "pair"), $4040$, $4141$, $4440$ (444 is not a "pair"). Accepted values: $4400, 4401, 0440, 4404, 4004$ Digits may be $0-9$, not just 4 and 0 etc.. So far I've got ($1 - 10P4 - 10 $) which is…
bg9848
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Color options for a flag

A flag has 3 horizontal stripes with a vertical bar on either side. With 10 different colors how many different ways are there to color this five region flag with no two touching regions the same. I get…
John Buer
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How many different number less than 600,000 - Permutation

I need to solve this task - Any help / direction would help me a lot. "How many different number less than 600,000 can be formed with digits 1,2,3,4,5,6; no digits repeated." I tried to solve it by using this formula: Using all digits (no repeats):…
Ilija Lončarević
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Permutation and Combination. Ordering people in a sample in groups then ordering the people in the groups

Suppose 100 students are in your school. The school’s principal wants to take photos of everybody in different ways so that every student thinks they’ve been treated fairly. a) The principal’s first idea is to take photos of every possible group…
Ike Casimir
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Number of permutation of $n$ objects when all objects are not different

In how many ways $5$ $A$'s and $6$ $B$'s be arranged in a queue so that it reads the same forward and backward? I got that middle letter will be $A$ so that $A$ and $B$ can be arranged symmetrically. But I am struggling to get the answer.
Harsh Vardhan
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Flag Permutations

From a collection of 5 different colors of flags(at least 5 flags of each color) how many different signals can be made by displaying them in a vertical line, using any number of flags from 1 to 5? I tried to answer like this: $$N=…
Madisson
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Permutation on sitting arrangement with conditions

Question -In how many ways can eight people be seated around the table if two people insist on sitting next to each other? Since the position of two people are known , i thought the answer would simply be 6!. Am i right teachers because i still have…
Dave
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Permutation on sitting arrangement

Question-In how many ways can eight people be seated around the table? As the question state only table, I do not know whether it is a rectangular table or circular table as the answer can differ from the category of the table. As for the circular…
Dave
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