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

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How to find different number of distinct integers fom given set of number

How many different integers can be expressed as the sum of $3$ distinct numbers from the set $\{3, 10, 17, 24, 31, 38, 45, 52\}$? Could someone help me with this problem?
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Inversion and permutations

Let call two arrays A and B with length n almost equal if for every i (1 <= i <= n) CA(A[i]) = CB(B[i]). CX[x] equal to number of index j (1 <=j <= n) such that X[j] < x. For two ...
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How to represent a problem of choosing one permutation over x different subsets of combinations?

I'm writing a computer program and I have problems understanding how to iterate this problem: 3 independent sets of numbers where I need to choose two out of three. That falls under simple category ...
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1answer
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Permutations in circular arrangements

I have another permutation question that I'm having trouble with; this time with circular arrangements: To a meeting involving four companies, each company sends three representatives -- the ...
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Permutation/factorial question

I have this question: How many numbers greater than 40 000 can be formed using the digits 2, 3, 4, 5 and 6 if each digit is used only once in each number? The first digit needs to either be ...
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1answer
16 views

Relationship between the probability two items in a list are correctly relatively ordered and the probability of any item being in the right place

Given a disordered list a of size n, and an ordering on the items of a, is there a relationship between the probability that two items are correctly ordered ($P(a_i \leq a_j)$ given $0 < i < j ...
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484 views

Permutation identities similar to $(7901234568 / 9876543210) \cdot 1234567890 = 0987654312$

It is well known that $9876543210/1234567890 = 109739369/13717421 = 8.0000000729...$ (See for example) Recently I posted at http://list.seqfan.eu/pipermail/seqfan/2012-October/010235.html my ...
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442 views

What do all the $k$-cycles in $S_n$ generate?

Why don't $3$-cycles generate the symmetric group? was asked earlier today. The proof is essentially that $3$-cycles are even permutations, and products of even permutations are even. So: do the ...
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Place, show and unordered horses forecast probability calculation

given the following horses, each with its chance of winning: Horse 1 -> 0.29 Horse 2 -> 0.34 Horse 3 -> 0.11 Horse 4 -> 0.07 Horse 5 -> 0.14 Horse 6 -> 0.05 Sum -> 1 At the moment, in order to ...
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63 views

Help calculating Combinations

A boy has n objects to paint, ordered in a row and numbered form left to right starting from 1. There are totally c colors, numbered from 0 to c-1. At the beginning all objects are colored in color ...
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Sum of possible permutations

Lets call two arrays A and B with length n almost equal if for every i (1 <= i <= n) CA(A[i]) = CB(B[i]). CX[x] equal to number of index j (1 <=j <= n) such that X[j] < x. For two ...
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how to find the root of permutation

Observe that $$\bigl(\begin{smallmatrix} 1 & 2 & 3 & 4 & 5 \\ 2 & 4 & 1 & 5 & 3 \end{smallmatrix}\bigr)* \bigl(\begin{smallmatrix} 1 & 2 & 3 & 4 & 5 \\ ...
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How many ways to arrange books? Combination/permutation problem

I'm having trouble solving this question...I'll try to be more specific. The problem could be split into 3 "cases" (4 bio, 3 bio+1 novel, 2 bio+2 novels) I used combination rule for 4 bio case and ...
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81 views

Arranging numbers in a grid

I have a $n \times m$ matrix $M$ and a permutation of sequence $P$ of numbers from $1$ to $n$. I have to fill the matrix using numbers $1$ to $n \times m$ in such a way that for each row $i$, the ...
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Counting Problem using Permutations

The Question was: In how many ways can the letters of the English alphabet be arranged so that there are exactly 10 letters between a and z? My approach was the following: In between a and z, there ...
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3answers
25 views

Problematic Permutation Problem

i see a problem without any definition. would you please help me? i want to calculate the number of permutations of 1,2,...,1392 that 696 numbers be in the natural positions (from all numbers, 696 ...
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3answers
68 views

Counting valid tickets

I think my question is very easy but I need to understand. The problem is, I have a ticket with 2 numbers from 1 to 10. The first number cannot be greather than the second number. How many valid ...
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3answers
20 views

Combination & permutation help!

I was thinking: 120 - 5C4 but the answer is 24. Is anyone able to explain this for me?
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36 views

How many even numbers greater than 50 000 can be formed from specified digits without repeat?

The digits are 3,4,5,6,7,0 My working is as follows: I realize that you would need to start with either 5,6 or 7. From there you have 5 digits to re-arrange, but the permutation would have to end in ...
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36 views

Total number of possible sub sequence with given condition

Given a sequence of two letters A and B find the total number of possible sub sequences where number of letter A is two times the number of letter B without ...
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1answer
29 views

Determining the different number of subsets (counting, permutations, combinations)

Given that any fixed integer n>0, let S={1,2,3,4,...,n}. Now a Red-Blue subset of S is called T. Every element of T is given a colour (either red or blue). For instance {17 (red)}, {1 (red), 5(red)} ...
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42 views

Permutations, Combinations, and Counting

A group of 63 people are camping together. They have two 6-person tents, three 4-person tents, five 3-person tents, and three 2 person tents. 18 people will sleep outside of the tents under a tarp. ...
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Permutation and Combinations (Separation) [closed]

Eight students are to be arranged in a row. Find the number of ways to arrange them if three particular students must be separated.
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45 views

Counting the arrangements of 8 people around a square table?

I am trying to solve this problem of counting the number of arrangements of 8 people around a square table, as shown in the figure below, To solve this problem you can consider arrangements obtained ...
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Permutation certification. A cryptographic hash function for permutations?

Alice has a secret permutation $\alpha$ (a random permutation of an $n$-set; $n=18$ would be a decent choice for the application I have in mind). She wants to convince Bob that she has $\alpha$, but ...
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40 views

Devise formula for Finding the number of permutations with repetition whose sum APPROACH a target number

Suppose a given set $s = \{2,3,4\}$ and lower limit $= 7$. I need to devise a formula for calculating the number of all possible permutations with repetition satisfying the following conditions: The ...
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135 views

Probability of $\alpha\beta\gamma=\gamma\beta\alpha$ for random permutations of a finite set?

Following up on my previous question Probability that two random permutations of an $n$-set commute?, here's a related question for three elements. Q: If $\alpha,\beta,\gamma$ are chosen uniformly ...
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23 views

How to calculate the HHG (Heller Heller Gorfine) correlation

HHG (A consistent multivariate test of association based on ranks of distances) is introduced in: Heller, R., Heller, Y., & Gorfine, M. (2012b). A consistent multivariate test of association ...
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Another formula for number of onto function.

Let A and B be two sets. $A=\{1,2,\dots m\}$ $B=\{1,2,\dots n\}$ We have to find the number of onto functions from A to B In the following link , the approach of the answer was applying Inclusion ...
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45 views

number of cycles in a permutation

I have given a permutation let 2 3 1 5 4 that is if initially my string is 1 2 3 4 5 the after one permutation it will become 1 2 3 4 5 3 1 2 5 4 that is the number in first position will go ...
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1answer
49 views

Partition numbers with restriction on the greatest part *and* on the number of positive parts

I’m looking at partition numbers. OEIS A008284 says that the number of partitions of $n$ in which the greatest part is $k$, $1 \le k \le n$, is equal to the number of partitions of $n$ into $k$ ...
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What Will be permutation of this question?

Sereja call two arrays A and B with length n almost equal if for every $\,i (1 \le i \le n), CA(A[i]) = CB(B[i])$. $CX[x]$ equal to number of index $j (1 \le j \le n)$ such that $X[j] < x$. For ...
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1answer
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If matrix $A$ is invertible, then there is a permutation of its rows leaving no-zeros on the diagonal

I need to prove this statement: "If $A$ invertible, then exist a permutation of its rows leaving no-zeros on the diagonal" and I tried using the definitos of invertible matrices and $LU$ ...
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Possible permutations of a 3x4 cube puzzle

My kids have this 3x4 cube puzzle, you know, the one where a picture is formed if you assemble the cubes correctly. In reality you can create 6 different pictures, using different sides of the cubes. ...
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How hard is this constrained $n$-rooks problem?

Suppose you have an ($n \times n$)-chessboard, together with a constraining function $C : n \times n \to 2$ where $C(i,j) = 1$ iff you're allowed to place a rook in the $ij$-square. Consider the ...
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Need help in confirming the answer to a combinatorics question?

I need help to confirm my answer for the following question "There is an alphabet of size 40 and this alphabet is used for forming messages in a communication system. If 10 of these alphabets can be ...
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89 views

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 ...
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30 views

Number of ways to order items

How many ways are there to put 10 red and 9 blue balls in a sequence so that for every index the number of red balls up to and including this ball is greater than the number of blue balls? It means ...
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31 views

No. of ways to arrange 4R and 3L so that there is exactly 4 times change from L to R or R to L.

I have to arrange 4R and 3L in such a way to know number of times there is 4 changes in the alphabet of sequence. For instance consider the sequence RLRLLRR, this sequence has 4 places where R and L ...
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32 views

Predict number of Birthdays for 1000 person of same class in next 365 Days

I want to know an approximate number of birthdays for a class where each month 1000 Persons are added up. Like 1st month its 1000, 2nd month its 2000, 3rd month it is 3000 And so on. Now lets say ...
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For $k$ random perms of an $n$-set $\mathrm{Pr}[\sigma_1\cdots\sigma_k=\sigma_k\cdots\sigma_1]\xrightarrow{k\rightarrow\infty}\frac{2}{n!}$?

Q. Fix $n \geq 2$, and choose $k$ random permutations $\sigma_1\sigma_2\cdots\sigma_k \in S_n$ uniformly at random. Is true that ...
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Probability that two random permutations of an $n$-set commute?

From this MathOverflow question: It is well known that two randomly chosen permutations of $n$ symbols commute with probability $p_n/n!$ where $p_n$ is the number of partitions of $n$. -- Benjamin ...
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3answers
52 views

Permutation & Combination Problem

I often solve math questions because I like it (This may sound crazy, I know :)). Today I came across an interesting permutation & combination question. The question is as follows: 6 people ...
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58 views

probability and combinations with the word REGULATIONS

If the letters of the word REGULATIONS are arranged at random,what is the probability that there will be exactly 4 letters between R and E? The answer in my book is given as 11!/(9C4 x 4! x6!x2!) ...
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How many matrices satisfy this condition?

Given the positive integer $N$ and $D$, generate all the non-negative integer matrices which satisfy matrix dimension is $N\times N$; sum of each row elements equals to $D$ sum of each column ...
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312 views

Permutations of a set with a conditional subset

Using the digits 1, 2, 3, 5, 6, 8, 0 only once, how many 4-digit numbers could be constructed if the number is even? This is an exercise from an online course I'm taking. The given solution suggests ...
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Number of unique permutations of a 3x3x3 cube

Given a 3x3x3 cube (like a rubik's cube) where each of the 27 cubes has a distinct number, how many unique permutations are possible? Simple rotations of the entire cube should not be counted. The ...
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Combination problem technique

How many numbers can be formed from 1, 2, 3, 4, 5 (without repetition), when the digit at the units place must be greater than that in the tenth place? It can be easily solved that, the total ...
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Factorial and combinations question.

Any help with these would be greatly appreciated... 1) How many arrangements are there of the letters of the word SAUSAGES ? if the A’s must be together and the S’s apart? (answer apparently 240 ...
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Mapping permutations with repetitions to an index

I am looking for a way to map permutation with repetitions written in big array (for example with million elemenths) to an index written in other array. Every element in array can have values from 0 ...