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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Why nothing taken from n things can have 1 permutation?

Without repeating if I take 0 thing out of n, how the permutation will be 1 (nP0 = 1)? And what will be that permutation? Even allowing repetition, the result is 1 (n^0 = 1)? How is the permutation 1 and what is that permutation?
Shuvo Sarker
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There are 11 members in a family out of which there are 4 males and remaining females

There are 11 members in a family out of which there are 4 males and remaining females. The family has hired three cars for a trip to zoo. The members are to be seated in the cars in such a way that there are not more than four members in one…
Kiran
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Disjoint cycle Decomposition.

Let $\sigma =(a_1...a_6)$ be a $6$-cycle. Write the disjoint cycle decomposition of $\sigma^2$ and $\sigma^3$. I know that $a_1*a_1=\epsilon $ but does this mean that $\sigma^2=\epsilon$ and then $\sigma^2=\sigma$ ?
Alex
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Simple permutation/combination question

In how many ways I can arrange six books on different subjects in a row such that the Math book is always to the left of history book (not necessarily adjacent) ?
user2434
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Why is $(13)(12)(13)^{-1}=(23)$?

I thought I understand how to multiply cyclic permutation, until I tried to determine what are the conjugates of $(12)$ in the symmetric group of three elements. In order to find the conjugate class of $(12)$, what I need to do is to find the…
Salech Alhasov
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Proving Property of Certain Permutation Groups

I'm trying to show that there is no $g$ such that $g^{-1}(1,2,3)g = (1,3)(5,7,8).$ I am having some general issues figuring out where to move with this problem, since it seems difficult to figure out how to make a contradictory statement to prove…
Melinda
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Permutation of the word mathematics

How many permutations are there of the letters Mathematics? (a)How many of them begin and end with letter A? (b)How many of them does not have two vowels adjacent to one another? For (a) I got 9!/4 For (b) I do not even know how to start...
luluja
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How many ways we can arrange 4 letters from PROFESSOR?

How many ways we can arrange 4 letters from PROFESSOR? The way I tried to do is by grouping the repeated words like (OO), (RR), (SS) and that can be done in three ways which seems to me a bit complicated and time consuming too. Can't we do…
Rayan Ahmed
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How many permutations are there of the letters, taken all at a time, if the word

How many permutations are there of the letters, taken all at a time, if the words (a) ASSESSES (b) PATTIVEERANPATTI Ans: (a) $$\frac{8!}{5!\cdot2!} = 168$$ (b) $$\frac{16!}{2!\cdot3!\cdot4!\cdot2!\cdot2!}$$ Are these the correct answers?
Raj
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Order of permutations

A pack of 2n cards is shuffled by the "interlacing" method, in other words, if the original order is 1, 2, 3, 4,...,2n, the new order after the shuffle is 1, n+1, 2, n+2,... n, 2n. Work out how many times this shuffle must be repeated before the…
Maths123
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The letters of the word REGAIN when arranged as per dictianory, find the 32nd word.

The letters of the word REGAIN when arranged as per dictianory, find the 32nd word. a)AEGIRN b)AEGRIN c)AEIGRN d)none of these MyApproach As per dictionary order, alphabets will follow the order AEGINR. Now,Starting with A,other letters will…
justin takro
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How many different integers can be expressed as the sum of three distinct numbers from the set{$13$,$10$,$23$,$28$,$33$,$36$,$43$,$48$}?

How many different integers can be expressed as the sum of three distinct numbers from the set{$13$,$10$,$23$,$28$,$33$,$36$,$43$,$48$}? MyApproach Out of $8$ numbers, Select $3$ distinct numbers. So Ans would be $8$C$3$=$56$-2=$54$. Because $2$…
justin takro
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In how many ways can we arrange 7 different things to 3 people all of them must get at least one.

In how many ways can we arrange 7 different things to 3 people. All of them must get at least one. My Approach I used the formula (n-$1$)C(r-$1$)=$6$C$2$=$15$ But I am confused will it work for different things also?
justin takro
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IN how many ways we can distribute 10 identical looking pencils given the following conditions?

IN how many ways we can distribute 10 identical looking pencils to 4 students so that each student get at least one pencil? a)5040 b)210 c)84 d)none of these MyApproach To distribute 10 identical pencils into 4 students,I first gave 4 pencils to 4…
justin takro
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When to use circular permutation vs when to use linear permutation?

I'm learning about permutations, both linear and circular. For most questions, I am spoon-fed whether the problem should use circular or linear permutation to solve. IE I'm told it's a ferris wheel or a necklace. However in the real world, I'm…
user2779949
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