Tagged Questions

For questions related to permutations, which can be viewed as re-ordering a collection of objects.

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Arrangement of 12 boys and 2 girls in a row.

12 boys and 2 girls in a row are to be seated in such a way that at least 3 boys are present between the 2 girls. My result: Total number of arrangements = 14! P1 = number of ways girls can sit ...
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No subgroup of $S_n$ containing stabilizier of 1?

Is it true that the stabilizer of $1\in \left\{1,\dots ,n \right\}$ in $S_n$ is a maximal subgroup? Intuitively I'm thinking that as soon as you add another permutation, you'll somehow be able to ...
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Number of zigzag permutations of first $n$ natural numbers given start and end value

Given $n$ and $1\le s,e\le n$, how to compute the number of zigzag permutations of first $n$ positive integers starting with $s$ and ending with $e$? I tried formulating a recurrence relation but can'...
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For the numbers $1, \ldots, N$, how many ways can I arrange them such that either: The number at $i$ is evenly divisible by $i$, or $i$ is evenly divisible by the number at $i$. Example: for N = 2$... 2answers 27 views Permutations & series [closed] Consider all the$7$-digit numbers containing each of the digits$1,2,3,4,5,6,7$exactly once, and not divisible by$5$. Arrange them in decreasing order. What is the$2015$th number (from the ... 1answer 22 views Concept of alike in Permutation and Combination Number of ways in which$7$green bottles and$8$blue bottles can be arranged in a row if exactly$1$pair of green bottles is side by side . (Assume all bottles to be alike except for the colour). ... 2answers 48 views Using the Binomial Identity, prove that${n\choose k}+2{n\choose k+1}+{n\choose k+2}={n+2\choose k+2}$Using the Binomial Identity, prove that: $${n\choose k}+2{n\choose k+1}+{n\choose k+2}={n+2\choose k+2}$$Because this is in the form of a Binomial Coefficient, I can break down the LHS further:$$\left(... 2answers 47 views How many integers can be formed by using exactly x 4's, y 5's, and z 6's if no other numbers are used? Can anyone tell me the total number of integers than can be formed by using exactly x 4's , y 5's and z 6's and no other numbers are used? For x=1, y=1, z=1, the total is 6 \... 1answer 27 views Cyclic permutation group example (n>1) I have googled around and haven't been able to find any examples of some S_n with n>1 that is a cyclic group. This may mean it is a dumb question, any help is appreciated. 1answer 521 views In S4, find all the even permutation and show that the set of odd permutations isn't stable for binary operations in S4. I want to find the even permutations of S_4 so i am supposed to find the transpositions right? but of what permutation exactly do i find the transpositions? And how do i know which ones are even? ... 1answer 32 views How to find number of integral solutions, containing large number of cases? Number of positive unequal integral solutions of the equation x+y+z=12 can be found out knowing the cases it involves: (1, 2, 9) , (1,3,8), (1,4,7), (1,5,6), (2,3,7), (2,4,6) and (3,4,5). Thus, ... 2answers 35 views Permutation of 2 or more groups while keeping the ordering of the groups I've been trying to get a general formula for this, but I couldn't find anything exactly what I need. What I want is, let's say we have 3 groups: (x,y,z),(a,b,c) and (k,l,m) What is the total number ... 1answer 35 views Can someone explain this proof of the relationship between chromatic number and independence number to me? I came across the following claim and proof in this paper, and I really don't follow. If G is a vertex-transitive graph with independence number \alpha and chromatic number \chi then n/α(G) ≤... 1answer 57 views Condition for a binary matrix to contain a permutation matrix I would like to know if there is any condition to check whether a binary matrix contains a permutation matrix of the same size. E.g.$$A_1=\pmatrix{1&1&1&1\\ 1&0&0&1\\ 1&0&... 1answer 44 views Combination Problem :$6$Countries ,$4$players from each country$6$Countries participate a world tournament . Each country has$4$players. One Cricket player , One Rugby player , one Volleyball player and one Football player. Need to select a team of$8$... 1answer 50 views Understand a part of the proof about permutations in a symmetric group on$n$elements Let$\sigma$be an even permutation in$S_n$($\sigma \in A_n$). Assume$\sigma = \tau\sigma\tau^{-1}$for some$\tau \in S_n$and assume that the type of$\sigma$consists of distinct odd integers. ... 1answer 901 views Circular Permutations With Repetitions (Mirrored Ignored) For Circular Permutations with unique elements (mirrored ignored) the answer is (n - 1)!/2 (pretty straight forward). However I cant seem to figure out how to calculate circular permutations with ... 0answers 22 views Consider the system S which can take n input parameters and each parameter can take on m values (a) What is the maximum number of pairs a single test case for this system can cover? "I know that there are m^n different combinations in this example, but i'm unsure how many pairs a single test ... 0answers 23 views Summation containing permutations. Given $$a_1< a_2<......< a_n$$ find a permutation$\sigma$maximizing the sum $$\sum_{i=1}^n {a_i \over \sigma(i)}$$ I can't figure our where to begin. I know that the solution is$\sigma=...
You are climbing a staircase. At each step, you can either make $1$ step climb, or make $2$ steps climb. Say a staircase of height of $3$. You can climb in $3$ ways $(1-1-1,\ 1-2,\ 2-1)$. Say a ...