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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Permutations and school timetable

If there are 6 periods in each working day of a school. In how many different ways can one arrange 5 subjects such that each subject is allowed at least one period? I tried this way- One of the six periods can be arranged in 5 ways and the remaining…
Achari S Ganesha
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Is this notation $\prod\limits_{k=k}^n k $ valid for expressing this product? (ways of arranging $k$ things in $n$ places)

I want to express how many ways you can arrange $k$ things in $n$ places. $$\prod\limits_{k=k}^n k = k (k+1) (k+2)\cdots(n-1) n$$ Edit (added) { The example from which I started thinking about this was placing 3 different letters(always placing each…
Alejandro Veltri
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How do I solve for n in this permutation question?

I have the following question: Solve for n: $$_nP_3 = 6_{n-1}P_2$$ I don't know how I should begin to tackle this problem? Any tips/help would be appreciated.
ComputerLocus
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How many different 4 digit combinations will include at least one 7, assuming numbers cannot repeat

I cannot get the correct answer - $2016$. What I have tried so far is thus: the number $7$ can occur $1, 2, 3,$ or $4$ times. Since it is a combination we do not care if the number starts with zero or not since it is a combination and not a number.…
Danny Watts
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Permutations of a word with repetitions and conditions

How many permutations of "committee" exist where is must not end in an e? I've been trying to figure out a possible angle of attack on this question. I've tried to say instead, "how many possible ways are there that do end in an e?". However, this…
ylun
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Decomposition of disjoint cycles

Work out the decomposition in disjoint cycles for the following. a) (14)(12345) = (15)(234) b) (12)(2345) = (12345) c) (12)(23)(34) = (14)(24) d) (13)(1234)(13) = (143)(2) Can anyone tell me if the parts a) and b) are correct? And can anyone…
user1523
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Very silly permutation question

Okay let me briefly explain my doubt. I'll explain some easy problems,so that you can study easily my mind and you can guess what confusion i might be going through right now. This may be silly.But please help me out. How do you permute the letters…
vaidy_mit
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Finding the probability that three friends get into the same group

I am stuck with the following problem: Students of a school are divided into $\,4\,$ groups. What is the probability that three friends get into the same group ? The options are : $\frac34$ $\frac13$ $\frac{1}{16}$ $\frac{1}{64}$ I think…
learner
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Gap in the proof that the parity of a permutation is fixed

Can someone fill the gap in the following proof, that the parity of the number of adjacent transpositions which yield a permutation $\pi$ is fixed ? In a course I took this was done in the following way: Let $\pi=\tau_1\ldots\tau_n =…
resu
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Restoring Permutations

I was curious if anyone knew of any proofs or knew of how one might go about proving problems involving restoring permutations. An example of the type of proof I am interested in is: Prove that any $\sigma \in S_4$ can be restored to the identity…
Ebearr
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arrangement of NOT sitting together

I have the following exercise. Please help me to solve it. Exercise. In how many ways can 3 men and 3 women be seated at a round table if (a) no restriction is imposed (b) 2 particular women must not sit together (c) each woman is to be between 2…
user16168
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why we can't divide by 2 in every case of circular permutation

In the case of a ring or necklace, we divide all possible outcomes by 2. Why not in the Round table case for instance, if we have $5$ distinct key rings on a table, all we have to do is $\frac{(5-1)!}{2}$ then why we can't divide by $2$ in the case…
Sobia khalid
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Number of ways of arranging 5 boys and 5 girls in a queue if Infront of each girl number of girls are more than or equal to the number of boys is

The number of ways of arranging 5 boys and 5 girls in a queue if infront of each girl number of girls are more than or equal to the number of boys is My try: I am sure that first person should be a girl. G _ _ _ _ _ _ _ _ _ Now second can be a…
Shlok Jain
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How do I find all the permutations of a list excluding cyclic permutations?

How do I find all the permutations of a list excluding cyclic permutations? This problem has arisen due to a coding project I'm working on. I'm currently unsure if this was more appropriate for the math stack exchange or the coding one however the…
Mixnik
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Which of the following numbers can be orders of a permutation $\sigma$ of $11$ symbols

Which of the following numbers can be orders of a permutation $\sigma$ of $11$ symbols, such that $\sigma$ does not fix any symbols? $1. \;18$ $2.\; 30$ $3.\;15$ $4.\; 28$ could any one just give me hints?
Myshkin
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