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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Calculate total number of combination of 4 characters having pattern as Letter-Number-Letter-Number

I need to know "How" to calculate total number of combinations that are possible to generate 4 character string having a pattern of Letter-Number-Letter-Number. The complexity are: strings should be unique, and vowels should be excluded (not to use…
GDG
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Permutation Problem with Given Numbers

Given the digits 0,2,5,6,9. A. How many 3-digit numbers can be formed if no two digits are to be the same? B. Of the numbers formed, how many are even? How many are odd? How many are greater than 600? C. How many 3-digit numbers if the digit may be…
Omni-
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Different arrangements - Permutation

Into how many different arrangements that look different can three identical trigonometry books, 4 identical calculus books, 5 identical algebra books be placed on a shelf?
Omni-
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Give the digits $0, 1, 2, 3, 4$, and $5$. How many four digit numbers can be formed if digits can be repeated and contain at least one digit $3$

Given the digits $0, 1, 2, 3, 4$, and $5$. How many four digit numbers can be formed if digits can be repeated and contain at least one digit $3$?
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Fraleigh Section 9 Question 27

Question 27 on Section 9 of Fraleigh 7th edition: Part (a) Asks us to prove that a permutation in $S_n$ can be written as a product of at most $n - 1$ transpositions. I feel that this is not true. There are endless counter examples to this. Simply…
user7348
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Permutations 1-line notation, and inverse

Write (15)(286)(479) in 1-line notation. Find the inverse of (15)(286)(479). Can anyone please help? Thank you.
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Disjoint cycle permutations

Work out the decomposition in disjoint cycles. I am working on disjoint cycles. I sometimes get confuse, so can anyone please check my work. A) $(13)(2345) $ I am starting from right to left So $2$ goes $3$, and $3$ goes to $1$. $(21)$ Then $3$ goes…
Naye
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Permutation on word if E,F,G have to stay in order

Im stuck on a problem which I have answered and need help to verifiy if I have done/understood it correctly. Problem If we have the following string: A,A,B,C,D,D,D,E,F,G How many ways are there to rearrange the letters if the Letters, E,F,G have to…
Krimson
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permutation problem. GMAT-related.

There are $3$ elves and $3$ dwarves and $6$ chairs. The elves and dwarves are trying to integrate with each other and will only sit next to someone of the opposite race and not next to their own kind. How many arrangements are there for them to sit…
Jwan622
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Number combination with groups and the smallest repetition possible

I need to create a equation to assign a number of phrases (variable A) to a a defined number of groups (variable B) and repeat these assignment each day, and repeat this operation along of time with the smallest (or most distant) repetition…
Eduardo
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Permutations from a set

Part of my problem is I can't figure out which question answers my problem. I'm not so familiar with the kind of math lingo that I know how to ask this question, so I'm gonna bumble my way through this as best I can. I have a set of 24 words - I'm…
Jack
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Is the approach to proving this expression for an n-choose-k algorithm correct?

I randomly encountered this post here, asking why this is true: def subset(n, k): if k == 0: return 1 if n == k: return 1 else: return subset(n-1, k-1) + subset(n-1, k) Without reading the answer, I tried to…
Xiphias
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Yet another Seating Arrangement Challenge

Not sure if this is the right place to ask this, but here goes (fingers crossed that someone can point me in the right direction): I am planning a singles "speed dating" type event, but it's a little bit complicated. Here's the requirements: 12 men…
Desperate
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Exponent of 7 in $ \binom {100}{50} $

What is the exponent of 7 in $ \dbinom {100}{50} $? It's a question from my exam today and I am completely unsure how to solve it It seems easy but any help would be appreciated
user34304
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In how many ways can $10$ adults and $5$ children stand in a line ...

In how many ways can $10$ adults and $5$ children stand in a line so that no two children are next to each other? My solution: $_A_A_A_A_A_A_A_A_A_A_$ So I'm trying to follow this example:Combination and Permutation, and…
user87274