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

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29 views

Given a particular order how many times will it appear in all the possible permutations it has?

I have $10$ different coloured balls. I'm interested in selling them in packs of $15$ and the order is important. I know there are $10^{15}$ different ways of arranging these balls if I include the ...
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3answers
44 views

linear algebra-permutation

Given the permutation $$\sigma = \begin{pmatrix} 1&2&3&4&5\\3&1&2&5&4\end{pmatrix}$$ the matrix A is defined to be the one whose i-th column is the $\sigma(i)$-th ...
3
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1answer
34 views

Bit string combinations [on hold]

My madam gave me these questions, can anybody help me? How many bit strings of length $8$ contain: a) exactly three 1s ? b) most three 1s? c) at least three 1s? d) an equal number of 0s and 1s?
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1answer
28 views

Number of ways to divide variables into two categories

I'm looking for a possible solution to find out the maximum number of combinations that can be derived from the given variables. If I'm not mistaken, I think permutations and combinations is the way ...
2
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0answers
40 views

Drawing a Truncated Octahedron

I'm trying to draw a truncated octahedron in MATLAB. This is also known as a permutahedron so my strategy is to link up all the vertices via adjacent transpositions of permutations in $S_4$. What I ...
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1answer
42 views

Maximum and average number of inversions in array by induction

Just for your information, an inversion in an array $a$ is any ordered pair of points $(i, j)$ where $i < j$ and $a_i > a_j$. I can prove the maximum and average number of inversions in an ...
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1answer
34 views

In how many ways can 5 distinct objects can be distributed. [closed]

In how many ways can 5 distinct objects can be distributed into 3 distinct boxes. Can you please help me?
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2answers
22 views

Number of ways to form two different committees

There are five employees willing to serve on one of two different committees. If each employee can only serve on one committee, how many possible ways are there for the openings on the ...
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1answer
40 views

Fundamental principale of permutations

I have just begin to learn about Permutation and combination. (Just learned definition and factorial.) In which i have learn: $\sideset{_n}{_r}P=n(n-1)(n+1) \dots (n-r+1)$, $r\le n$ where ...
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1answer
35 views

Cardinal Arithmetic and a permutation function.

I am working on the following problem and am having difficulties getting started: We define a permutation of $K$ to be any one-to-one function from $K$ onto $K$. We can then define the factorial ...
0
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1answer
80 views

How does $A_n$ look in Aut$(X)$?

Let me phrase my question precisely: Let $X=\{1,2,3,...,n\}$, $ \ S_n=\mbox{Sym}\{1,2,3,...,n\}$ be symmetric group on $n-$letters. Let $\mbox{Aut}(X)$ denote the automorphism group of $X$. We ...
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1answer
55 views

distribution of books among students

There are $p$ students and $q$ books where $q>p$ and all books are different, but each student will get a minimum of $1$ book and a maximum of $(p – 1)$ books. Find the total number of ways of ...
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1answer
35 views

Number of ways to choose 6 cards with the same suit from a normal deck of cards

In how many ways can one choose 6 cards from a normal deck of cards so as to have all suits present? One way was $\binom{13}{1}\binom{13}{1}\binom{13}{1}\binom{13}{1}$ but it involves repetition of ...
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0answers
27 views

What's the name of $\sum_{k = 0}^{n} (-1)^k {n \choose k} (n-k)^w$?

I worked out the following expression as the number of all possible "words" consisting of exactly $w$ letters from an alphabet $L$ of size $\left|L\right| = n \leq w$, and containing each of these $n$ ...
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1answer
28 views

Count ways to sit men women in row of size K

Suppose we are given N men and M women.They are to sit in a row of size K such that no two women sit next to each other.What are the number of ways. Like if suppose their are 3 men and 2 women and ...
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2answers
55 views

Question of Permutation and combination

I have found a question from somewhere in the internet as follows: English language has 26 alphabets, out of 4 distinct vowels and 7 distinct consonants, how many letter patterns can be made ...
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1answer
43 views

Permutation as a product of transposition

I'm trying to figure out how the proof of the following theorem works: THEOREM: Every permutation is a product of transpositions. The proof is based on noetherian induction. I don't understand how it ...
0
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1answer
18 views

How Many Unique Character String Can Be Made From 62 Characters?

I'm working on a programming algorithm and need a little math help. I'm in 10th grade and I think the question I'm asking is actually a permutation and combination logic question. Okay, so I've 62 ...
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0answers
17 views

'Canonical' form of permutations, product of transpositions

I have such 'canonical' form of permutations: $\prod_{i=0}^n (i \ k_i)$, where $i \leq k_i \leq n$. For example, there are all $6$ permutations of $3$ elements. Of course, some transpositions do ...
6
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1answer
32 views

Equivalent of a sequence in regard to a certain length of a cycle for $\mathfrak{S}_{n}$

Let $n \in \Bbb{N}$ ( for me $0\notin \Bbb{N})$. Find the limit as $n$ tends to $+ \infty$ of the following sequence $$\frac{\alpha_{n}}{n}$$ where $\alpha_{n}$ is the number of permutations of ...
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3answers
45 views

Number of license plates formed by four digits and one letter, qualified.

I need some help with this question: If a license plate for a vehicle consist of five characters: $4$ digits (the first of which cannot be $0$), followed by one letter of the alphabet (which ...
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0answers
41 views

Finding different sum factors of a number

Actual Question : A fair die is thrown k times. What is the probability of sum of k throws to be equal to a number n? My Work: Lets have k buckets, fill-in each bucket with value(1-6) so that the sum ...
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3answers
46 views

What should n be so that the probability is less than 0.5 [duplicate]

n represents the number of people. The probability is that none of these people have a birthday on the same day. Neglect people that are born on 29 February. What should n be so that the ...
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0answers
12 views

How to run a number of tests with differing transitions?

I believe this would be the correct exchange to ask this question. I have a black box with 3 dials, a button, and a display. Each of the dials can be spun to be set to a number on that dial. The ...
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1answer
47 views

Where can I find a set of probability problems?

Is there a database of solved probability problems available? I am currently studying probability (and statistics) and, while I think I have a decent grasp of permutations, combinations, conditional ...
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3answers
122 views

Number of elements of order $2$ in $S_n$

How many elements of order $2$ are there in $S_n$? Using combinatorics I arrived at this: For $n$ even ($n=2k$) there are ${n\choose2}+{n\choose 2}{n-2\choose 2}\dfrac{1}{2!}+{n\choose 2} ...
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0answers
247 views

Sorting of prime gaps

Let $g_n $ be the $n^{th}$ prime gap $p_{n+1}-p_n.$ If we re-arrange the sequence $ (g_n)$ so that for any finite $n$ the gaps are arranged from smallest to largest we have a new sequence ...
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0answers
21 views

Couldn't understand the Rysers method for Permanent calculation

I am not that good in Mathematics. I am trying to understand since yesterday. Please someone help me out. Especially the second summation part in the right hand side. Ryser's method for permanent ...
2
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0answers
71 views

permutation and combination advanced

I have n sets having values less than 100. I need to find how many arrangements could be made if I pick one element from each set such that in the given arrangement there are no duplicates? NOTE: A ...
3
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3answers
36 views

Number of $r$ letter words taking letters from a $n$ letter word

I can't figure out how to do questions such as this one, any thoughts? What is the number of four letter words that can be formed from the letters in BUBBLE ...
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0answers
13 views

How to write a function or script uisng python to create the specific permutation on a set of numbers in tuples

(5,6,7),(8,9,10),(11,12,13) the above is the given set of number that define in 3 tuples. The desired permutation should be able to gives result as below. (5,6,7),(8,9,11),(10,12,13) ...
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2answers
92 views

Seemingly simple combinatorial problem

Count all $n$-length strings of digits $0, 1,\dots, m$ that have an equal number of $0$'s and $1$'s. Is there a closed form expression?
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0answers
37 views

Riemann Integrability over [1,5]

I am trying to design a question that makes sense. First, I consider the greatest integer function on an interval$ [1,5]$. This throws up $1,2,3,4$ and $5$. Then I wish to permute these numbers by ...
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3answers
25 views

The number of permutations with a distance condition

How can I think about this question: I have a string of As and Bs and I want the number of permutations such that the distance between two Bs is at least 2 ...
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5answers
64 views

Permutations of $9$ balls of $3$ colors [closed]

I have $9$ balls total, $3$ red balls, $3$ green balls and $3$ blue balls. How many ways I can arrange them?
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1answer
16 views

Predicting how long the result of a permutation

We're calculating the result of a 'tweaked' Birthday Problem, but when we're calculating, we stumped by a very nasty permutation. $$10^{576}P_{10^{16}}$$ Which, make us stop working at the number, ...
0
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1answer
15 views

Tag Rugby: 6 men a side, 4 on pitch, 2 subs. 40 minute game. How often to sub?

Playing a game of Tag Rugby tonight. We have 6 male players, of which 4 will always be on the pitch, with 2 subs. The game lasts 40 minutes, 20 each half. How long should each player get to play, ...
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1answer
35 views

Odds to guess a 32 byte value [closed]

I have 1,000,000 records, and each is assigned a 32 byte (3.4E+38) random value. What is the likelihood to guess one of the random values? Context This comes up in information security context: ...
3
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2answers
48 views

How many $3$ letter “words” consisting of at least $1$ vowel and $1$ consonant can be made from the letters of EQUATION?

The word EQUATION contains all five vowels. How many $3$ letter "words" consisting of at least $1$ vowel and $1$ consonant can be made from the letters of EQUATION? Hi, would anyone be able to ...
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3answers
27 views

Counting how many numbers have repeated digits

How many numbers are there in all from $6000$ to $6999$ (both $6000$ and $6999$ included) having at least one of their digits repeated ? (a) $216$ (b) $356$ (c) $496$ (d) $504$
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1answer
69 views

A 4 digits number is formed using 2,3,5,7 and 9 without repeat

A 4 digits number is formed using 2,3,5,7 and 9 without repeat. How many 4 digit numbers are there if each number has a remainder of 2 when divided either by 3 or 5? As i know, 2,3,5,7 and 9 is ...
2
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1answer
98 views

Number of ways possible to form a number?

Suppose we need to form a 4 digit number with the restriction that ...
0
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1answer
58 views

Number of ways by which we can form a n digit number such that no two digit are same in the number?

Example : 2 digit number : so all two digit number except 11 22 33 44 55 66 77 88 99...this is simple but how to generalize for a number of n digit?(Also at each place any digit from 0 to 9 can come ...
4
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1answer
54 views

How to check if $\text{position}\left(\frac{a + b} 2\right )$ is in range $\text{position}\left(a\right )$ and $\text{position}\left(b\right )$

Given a permutation of $n$ number $1, 2, 3,\dots,n$. How to check if it is exist $a,\ b$ with the same parity such that $\frac {a + b} 2$ is between $a, b$. How to solve this problem efficiently ? ...
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3answers
77 views

Intuitive explanation of even/odd permutation

Given a permutation it can be classified as either even or odd depending on whether it is expressible as a product of even or odd number of transpositions. Is there some geometrical or intuitive ...
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3answers
45 views

What is the minimum number of colours needed for coding 12 objects, if each may be marked with either one or two colours?

I have a word problem here which is a kind of high level to me A company that ships boxes to a total of (12) distribution centres uses colour coding to identify each centre. If either a single ...
0
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0answers
42 views

Number of possible ways to give change for 2 pounds

I was solving the following question on Project Euler In England the currency is made up of pound, £, and pence, p, and there are eight coins in general circulation: 1p, 2p, 5p, 10p, 20p, ...
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0answers
58 views

Sparse matrix algorithms involving data-driven or random access / walk

I am looking for some well-known algorithms in which sparse matrix elements are accessed in a non-structured way, i.e. row/column depends on a value of another (sparse) matrix/vector element or some ...
0
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0answers
54 views

The probability of random permutation leaving the sequence almost unchanged

So let's say I have $52$ completely different kinds of arenas that get shuffled. What are the chances of getting the exact same sequence if only one arena can be out of order? For example, you could ...
0
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2answers
34 views

Permutation and Combination with restrictions

There are 7 chairs. 4 are reserved for men and 2 are reserved for ladies. Remaining 1 can be occupied by anybody - either a lady or a man. In how many ways, can 6 men and 3 ladies be seated on ...