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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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How many permutations are there of the digits 1, 6 and any number of 0's between 213 and 5127

Working out the permutations by hand (I organized it by deciding where to put the 0's), I get 5 valid outcomes (out of 12 total = 3! * 2!) that are between 213 and 5127. I'm trying to figure out if I think of the numbers as symbols rather than…
Zev
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Finding exponent of a prime in $100!$

If $100!=2^m.I$ (Where $"I"$ is multiplication of odd numbers) then find the value of $"m"$
lucky jarolia
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Ten people are seated at a rectangular table - Permutations homework

I got the following question for homework. Ten people are to be seated at a rectangular table for dinner. Tanya will sit at the head of the table. Henry must not sit beside either Wilson or Nancy. In how many ways can the people be seated…
Jeel Shah
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Sign of composition of two different permutations

Does the following make sense? Let $\sigma\in S_n$ and $\pi\in S_m$. Then sgn$(\sigma\circ\pi)=$sgn$(\sigma)$sgn$(\pi)$. If it's nonsense, is there any wasy to we split sgn$(\sigma\circ\pi)$?
user344662
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Permutation and Combinations Choosing out of a Pool of People

Two students are to be randomly selected from a pool of N students, n of whom study maths. If it is known that at least one student studies maths, what is the chance that both students study mathematics? A.$$\frac {n-1} {2N-n-1} $$ B.$$\frac {n-1}…
D.Ronald
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How to calculate permutations when group is larger than set of characters?

I have a set of 71 ASCII characters that I use to assemble 192 character tokens. I need to calculate the number of permutations (as characters can repeat). The factorial of 192 is so large my computer kacked on it after $$10^{303}$$. I tried this…
TorontoJim
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How many even numbers larger than $60~000$ can be formed using the digits $1, 2, 3, 5, 6, 8, 9$ without repetition?

The $7$ digits $1, 2, 3, 5, 6, 8, 9$ are to be used to make $5$ digit numbers with each being used not more than once in a number. How many numbers can be made which are more than 60 000 AND even? I got something like $3\cdot 3\cdot 5P_3 = 540$. But…
mbkoverflow
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Let $X = \{1, 2, 3\}$, then why is $(1 \mapsto 2, 2 \mapsto 3)$ not a permutation?

I am learning some basic group theory, and just getting my head around permutations. In particular, I want to consider the counter-example noted in the title. Let $X = \{1, 2, 3\}$, then why is $\sigma$, where $$ \sigma = \left(\begin{matrix} 1 & 2…
bzm3r
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How many different words can be formed with all the letters of the word "INTERNET" if each word is to begin with vowel?

Plead help me to figure out the solution! According to the book it's answer is 1890. Please help me!
Bill
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Of the numbers formed by using all the figures 1, 2, 3, 4, 5, 6 only once, how many are even?

It is a question from permutations and combination chapter and its ans is 48 as given in book! Please help me to do this. I am unable to figure out the solution! Please help!
Fred
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how is permutation built from two given sets?

1- have two sets: set A containing $k$ numbers and set B containing $m$ numbers. want to build a set c whose elements are a pair $(i,j)$ where $i$ belongs to A and $j$ belongs to B. Permutation says the set C would contain $\frac{(k+m)!}{k!m!}$ how…
bijan karimi
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All the permutations that commute with (1 2)(3 4 5) in $S_5$

Determine all the permutations $\sigma \in S_5$ that commute with the permutation $\alpha = (1 \space 2)(3 \space 4 \space 5).$
H. Daniel
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Binary Permutations With Restriction

I have a random binary string of N bits with N/2 bits are one and N/2 bits are zero and the bits are generated by coin tossing so they have entropy N. Now I feed the bits to a deterministic algorithm that generates psuedorandom permutations of these…
William Hird
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Find the value(s) of $n$ that satisfy the equation $P(n, 3) = 8n + P(n, 2)$

Find the value(s) of $n$ that satisfy the equation $P(n, 3) = 8n + P(n, 2)$ where $P(n,k)=\frac{n!}{(n-k)!}$. So far I have : $$P(n,3) = 8n + P(n, 2) =8n + n(n-1) =7n + n^2 $$ How do I expand $P(n,3)$?
lollol12345
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A Random number generator generates only +1/-1. After 6 trials, which are independent, what is the probability that the sum of outcomes will be zero?

I have proceeded as follows: We need exactly 3 +1s, which could be in any order. So permutation comes into mind. What is wrong, and how should I proceed next?
Hansatanu Roy
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