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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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Permutations with repeated objects

In school $100$ kids are making necklaces from $11$ beads. Every kid gets this same set of beads: red , green, blue. Choose the sets which allow every kid to make different necklace: a) 7-red, 2-green, 2-green b) 7-red, 3-green, 1-blue c) 6-red,…
MatNovice
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Total Possible Combinations For this Pattern

If a string is to be generated with exactly 16 characters and it takes the following form: aaaaa####aaaaaa Where a is any of the 26 lower case letters and # is a number from 0-9 inclusive. How many possible combinations are there? If they were all…
NULL
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Permutations of a sequence

"Given a set $\{1,\ 2,\ 3,\ 4\}$, how many sequences with a length of $4$ with entries from this set have exactly one entry equal to $1$?" Here is my work so far: $$X = \left\{\text{sequences with length 4 from}\ \{1, 2, 3, 4\}\ \text{with exactly…
user41419
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Ratio of number of rectangles and number of squares in a chess board

We have to find the Ratio of number of rectangles (not squares) and number of squares in a chess board. For this type of question do we have to manually count the squares and rectangles or is there any other method?
Icandoahandstand99
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Number of possible permutations

So I just finished working out a probability question which I came across on the Brilliant website, where there is a game of tennis that finishes when someone reaches four points (ignoring deuces, it's just the first person to reach 4 points).…
Etched
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Let $S_{10}$ denote the permutation of $10$ symbols.Then the number of elements of $S_{10}$ that commutute to $(1 3 5 7 9 )$

Let $S_{10}$ denote the permutation of $10$ symbols.Then the number of elements of $S_{10}$ that commutute to $(1 3 5 7 9 )$ is a)$5!$ b)$5\cdot 5!$ c)$5! \cdot 5!$ d)$\frac{10!}{5!}$
Halima.Khatun
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The Number of quotient group of $S_4$ (the symmetric group of 4 symbols) up to isomorphism

The Number of quotient group of $S_4$ (the symmetric group of $4$ symbols) up to isomorphism is/are a)$1$ b)$2$ c)$3$ d)$4$
Arib khan
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Number of n digits having no same consecutive digits and same first and last digit

We have to form a number of n digits having digits from 1 to 9. Constraint is that first and last digit must be same and no two consecutive digits must be same. How many such number of n digits can be there?
Shashwat Kumar
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Number of ways of selecting 4 numbers from 20 numbers under certain condition

Out of 20 consecutive natural numbers, in how many ways 4 numbers can be selected such that any two selected number differ by at least 3. I am not able to proceed further than writing domain of each number( x, y, z, w be the numbers in increasing…
alekhine
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number of possible arrangements

There are $n$ identical red balls & $m$ identical green balls. The number of different linear arrangements consisting of "$n$ red balls but not necessarily all the green balls" is $\binom{x}{y}$. Find $x$ and $y$.
Anuj
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Permutation problem - 8 letters

I need to solve this problem but I do not know how. Sherlock Holmes and Dr. Watson have on the fridge magnets with a series of eight letters. It is an eight different letters. Every morning Sherlock swapped letters first to the seventh, eighth with…
davidson94
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How would one answer this simple permutations question?

You deal 7 cards off of a 52-card deck and line them up in a row. How many possible lineups are there in which no card is a club or no card is red? My answer was $P(13,7)$ which is incorrect according to my book.
ClownInTheMoon
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Show $f \in S_4$ does not generate the whole $S_4$

I want to show that $f \in S_4$ does not generate the whole $S_4$, that is $\{f^k\mid k\in \mathbb{N}\}$ is not the whole $S_4$. I think of the possible disjoint cycle structures $f$ can have: i) one 4-cycle such as $(1 2 3 4)$, ii) one 3-cycle and…
user30523
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Number of possibilites for $4$ digit code with two identical digits

We have $4$ digit code or number. Every digit can be integers from $[0,5]$, i.e. $6$ different values. Question is two find number of possibilities where exactly two of the digits are the same. e.g. 1231,1132,2311,..are some of results.
Heyro
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Transpositions to work out odd/even permutations

When working out the transpositions on simple permutations, e.g. a = (1 2 5 4 3) I know that a = (13)(14)(15)(12) so it is even However I cant find transpositions of permutations that overlap, e.g say a = (1 2 3 4)(4 5 6)(2 5 3), I want to…
MooeSha123
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