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 many numbers are there between 100 and 1000 in which all the digits are distinct?

How many numbers are there between 100 and 1000 in which all the digits are distinct? My mathematics textbook says the answer is 648. My analysis:- The number at the hundred's place can be chosen in 9 ways(as zero is not possible) The number at the…
Abhishek Mhatre
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How many permutations when each position takes from different length alphabets?

Let's say there's a password scheme as follows: the password is of length 4 (four) the 1st position is taken by one character from the set: a, b, c the 2nd position is taken by one character from the set: D, E, F, G the 3rd position is taken by one…
user664833
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A puzzle in Permutation.

There are two stacks A and B. A : a,b,c,d ('a' is on top and 'd' is at the bottom of the stack) B : (empty) There are two rules. If an element of A is popped, it must be printed immediately or pushed into B. If an element of B is popped, it…
Vishnu Vivek
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About Constrained permutation

In how many ways 'n' distinct objects can be distributed among 'm' group where each group will get at most 'k' objects (it is possible that one can get no object)?? Thanks In Advance. Example: (1) n=3 m=3 k=1 ways=1 ,i.e (1,1,1) …
JYOTIRMAY SAHOO
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Is this "distance" measure between permutations a metric?

Take $f,g\in S_n$, the symmetric group on a set $X$ of size $n$. Define the function $$d(f, g) = n - |\{x\in X : f(x) = g(x)\}|$$ In words, this defines a distance on permutations by how many inputs they map to the same output. This is kind of a…
pg1989
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Permutations of $3$ elements which sum to $100$

I need to find the number of permutations of $3$ elements which add up to $100$. For each element, $0 \leq x \leq 100$. So we could have $0,0,100$; $1,0,99$; $0,1,99$ etc. Order is important - I need to count $1,0,99$ as well as $0,1,99$. Can anyone…
ZebE
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Are there multiple ways to translate a permutation $\alpha$ to a permutation $\beta$?

Are there multiple ways to translate a permutation $\alpha$ to a permutation $\beta$? I came across the question below and found multiple solutions for $\gamma$. My approach to finding solutions is not very rigorous, but I did check my answers and…
Zaz
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Permute Infinite Set

While thinking about permuting(arrange elements in order in a given set), this is available always for finite sets and this fact could be proven by mathematical induction. However, when to think about permuting of infinite set, it is unsure of…
Beverlie
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Number of permutations of $4$-digit password lock given that it must contains the digits $1$, $2$, and $3$

Password has $4$ digits Each placeholder can take value from $0$ to $9$ Must contain digits ($1$ AND $2$ AND $3$) Valid sequences are ($1123, 0231, 1023, \ldots$) Invalid sequences are ($0010, 9999, 0023, \ldots$) How many valid permutations are…
Zanko
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Find the ways in which no husband can sit next to another husband

A group of 6 people consisting 3 married couples are to be seated together in a straight row. How many different ways are there of seating the 6 people if no husband is to sit next to another husband? Since the husbands can't sit next to each other,…
XxS0ul678
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How to calculate the number of total permutations of a set excluding some results?

I have to calculate the number of total permutations that are possible to obtain from a set of objects (position of balls), excluding some results. The problem The main 'object' is a set of 2 balls that are connected by a string (so it forms a…
Richard Steele
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Recurrence relation for Number of permutations with constraints of a combination of symbols

Suppose we have $m+n$ symbols out which $m$ are identical and $n$ are distinct. It is required to find the number of permutations of these $m+n$ symbols such that no two identical symbols are together. I tried to solve it through the help of …
AgnostMystic
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From $3$ red, $4$ green and $5$ yellow balls, how many selections consisting of $6$ balls are possible, if each color must be represented twice?

From $3$ red, $4$ green and $5$ yellow balls, how many selections consisting of $6$ balls are possible, if each color must be represented twice?
Santiago Bueno
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The number of triangles with each side having integral length...

The number of triangles with each side having integral length and the longest side is of 11 units is:-? MY ATTEMPT:- I applied following constraints: $12 \leq {a+b} \leq 22$ $a,b \geq 1$ I made different cases that a+b =12, a+b=13 and so on. My…
Ruchit Vithani
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taking seats probability in a room

In a room with $k$ chairs in a circle, $m$ men and $w$ women take seats, where $m+w=k$. What is the probability that every man has a woman on his left and right? kind of lost here.
Nikko
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