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

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Counting the number of permutations and combinations

How many numbers consisting of five digits each can be made from the digits $1,2,3,\ldots,9$ if (a) the numbers must be odd (b) the first two digits of each number are even. ...
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2answers
123 views

What is the number of permutations for given N numbers, such that the first part is non-decreasing?

Let $A$ be a list of $n$ numbers in range $[1,100]$ (numbers can repeat). I'm looking for the number of permutations of $A$ which start with a non-decreasing part, where this part ends with the first ...
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1answer
43 views

Permutations using coefficient method [duplicate]

I had a question which is as follows:Number of words of 4 letters formed using the word IITJEE.The book says the answer as coefficient of $x^4$ in 4!$\mathrm{[1+ \frac ...
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2answers
137 views

Permutation & Combination card sequence . .

I've been trying to do these 2 questions about Permutation & Combination which linked to card play. Q1 says : ...
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2answers
112 views

How many ways to split n elements in k groups? [duplicate]

The order of the groups does not matter The size of group must be at least 1 For example, in a more specific question How many ways to split 5 number in 2 groups?, we got the answer 15 from Jared, ...
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2answers
49 views

Ways to select three-man teams

In a competition there are 18 competitors. Answer the following: A) During the first day they're competing in three-man teams (total of 6 teams). How many ways are there to select the teams? B) If ...
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1answer
48 views

A question on a matrix built with permutations of the $n$ first integers.

Let each row and each column of a $n \times n$ matrix $A$ be a permutation of $\{1, 2,...n\}$ and let $A$ be symmetric. (a) If $n$ is odd, prove that each of $1, 2,..., n$ occurs on the principle ...
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2answers
32 views

Perfect shuffle of 52 cards

Prove: How many perfect shuffles of a deck of 52 cards do you need to do until the deck returns to its original order? Can anyone please help me prove this? Attempt: I have tried putting the deck of ...
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1answer
59 views

Explanation of basic definitions in game theory.

In the article entitled Non-Cooperative Game written by Nash in 1951, he discussed about the symmetries of games. Due to my lack of basic knowledge in permutations and symmetries, I looked up some ...
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1answer
41 views

Permuation, disjoint cycles proof by induction.

I am having a hard time writing out a general proof. Can anyone please help? Thank you. Exercise: Show that any k-cycle (a1,......,ak) can be written as a product of some number of (k-1) 2-cycles. ...
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0answers
36 views

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 ...
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3answers
25 views

Permutations 1-line notation, and inverse

Write (15)(286)(479) in 1-line notation. Find the inverse of (15)(286)(479). Can anyone please help? Thank you.
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2answers
78 views

Show that $\sigma^2$ is a Cycle iff the length of $\sigma$ is Odd

I got this question. I'm totally stumped and I don't know what to do. Let $\sigma$ be a cycle of length $k > 2$. Show that $\sigma^2$ is a cycle iff $k$ is odd.
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1answer
44 views

Why is the order of a $k$-cycle $\sigma$ equal to $k$?

If $\sigma = (a_1,a_2,\ldots,a_k)$, then the order of $\sigma$ is $k$ because $\sigma^k = Id$. I've tried finding a proof on the internet, but all sources just say "it's clear that", etc. I'm probably ...
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2answers
119 views

combination and permutation !!!!

I have 3 questions that i had a try to do but i didn't understand them could anybody please help me to solve these questions. For Q1 i know how to use the multiplication counting procedures for a) i ...
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1answer
88 views

Exotic 6-horse race betting probabilities

I'm gearing up for horse racing season, and I'm trying to teach some fellow engineering friends how to bet "exotic" bets by using colored dice to simulate horses. So, the odds for each horse winning ...
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2answers
29 views

Disjoint cycle permutations

Work out the decomposition in disjoint cycles. I am working on disjoint cycles. I sometimes get confuse, so can anyone please check my work. A) $(13)(2345) $ I am starting from right to left So $2$ ...
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1answer
19 views

Permutation problem in language

A language has 28 letters. Each word in the language consist of maximum 7 letters. How many maximum combinations letters can be framed. Provided the letters can be repeated.
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1answer
34 views

Combinations or Permutations of bits

I am a computer science major and was explaining to someone how a computer uses bits to represent numbers. If you have 1 bit, you can have 0 or 1. With 2 bits, you can have 00, 01, 10, 11, or 0, 1, ...
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0answers
55 views

Symmetric Group $S_3$

I just wanted to make sure I am thinking about this correctly. I would like to take the product $(123)(231)$. Here, $2-3-1,3-1-2,1-2-3 \Rightarrow (123)(231)=(132)$.
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2answers
53 views

Permutations product

Can anyone please help me compute $513642798 \times 971265384$ attempt: I start with the right permutation, So $9 \to 7 \to 9 = (97)$ however, after that do i go to $7 \to 1 \to 3$ ...? I am ...
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4answers
62 views

Permutation on word if E,F,G have to stay in order

Im stuck on a problem which I have answered and need help to verifiy if I have done/understood it correctly. Problem If we have the following string: ...
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1answer
31 views

permutations of “optimization”

How many permutations of the word optimization are there? I get confused with the repetition of the letters. If all 12 letters were distinct, then we would have 12! Because 4 letters are repeated, I ...
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0answers
231 views

Finding the number of arrangement of N people of different height such that K of them are visible from front

Moderator Note: This is a current contest question on codechef.com. [Initially, I had asked this question in stackoverflow, but someone suggested to post it here, and hence this question is ...
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1answer
270 views

Find total perfect combinations

Suppose we are given N numbers and a value K. Now we can interchange the positions of numbers to form different combinations, where if there are two same numbers then their arrangments will be ...
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2answers
38 views

combinatorics - permutations question, possibly with pigeon hole

Let $A \in Mat_n(\mathbb R)$ such that $\forall i,j: a_{ij}\geq 0$ We are given: $$\forall j: \sum_{i=1}^n a_{ij}=\sum_{i=1}^n a_{ji}=1$$ show there's a permutation $\pi \in S_n$ such that $$\forall ...
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1answer
34 views

Permutation of a 4 character string made up of letters and numbers

This is a straightforward question but I didn't pay attention in school. I want to know how many permutations there are for a 4 charcter string made up of numbers and letters. After a quick look ...
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0answers
36 views

Notation for number of tensor permutations

I have a tensor (or set if you will) that consists of N elements, and each element has a limited number of values it can take. For example: ...
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2answers
157 views

Number of bitstrings with $000$ as substring

I have $F_n$ number of bitstrings that have $000$, How would I prove that for $n \ge 4$ , $a_n = a_{n-1} +a_{n-2}+a_{n-3}+ 2^{n-3}$? Now there are many ways to go about this but if I choose starting ...
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1answer
40 views

Combinatorics - inclusion exclusion, check my answer

It's my second try to solve the question I posted here Combinatorics question - How many different ways to change sitting order I got some really good advice, but no one said the answer, I solved it, ...
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0answers
28 views

Number of permutations, but constricted number of possible to take

I'm looking for the general formula to calculate: take x items but at most y of each and there is z types of items My specific problem is: ...
0
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1answer
39 views

permutations of a 3 object

Help please, Exercise: Work out the full multiplication table for the set of permutations of three objects. I know there are 6 permutations. (1,2,3), (2,3,1), (3,1,2), (2,1,3), (1,3,2) and (3,2,1). ...
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2answers
53 views

Probability and combination/permutation help? [closed]

So, I need some help on a few problems. This isn't my homework. I'm preparing for a test and these are just some of the practice problems. I have the answer for them but I don't understand how to get ...
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1answer
104 views

proving bitstrings [duplicate]

1.Let it be $a_n$ the number of bitstrings which contain 000 How would I prove that for $n\ge4$: $$a_n = a_{(n-1)} + a_{(n-2)} + a_{(n-3)} + 2^{n-3}$$
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1answer
27 views

permutation problem. GMAT-related.

There are 3 elves and 3 dwarves and 6 chairs. The elves and dwarves are trying to integrate with each other and will only sit next to someone of the opposite race and not next to their own kind. How ...
2
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1answer
30 views

simple combinatorics question - what did I do wrong?

I was asked the following question. I solved it, I thought my solution is correct, but it turns out I was mistaken, I'd like to know why. Question: How many ways are to order 4 sets $(A,B,C,D)$ such ...
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1answer
30 views

A committee of 12 is to be formed from nine women and eight men. In how many ways can this ..

Problem : A committee of 12 is to be formed from nine women and eight men. In how many ways can this be done if at least five women have to be included in a committee ? Solution : Case I : 5 W ...
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2answers
63 views

Calculate product of transpositions

I've searched for this kind of question-answer, but didn't managed to find one because the problem is quite specific. Let me explain: I have permutation: $(13927)(5846)$ which I must write as ...
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1answer
40 views

Probability of all objects not in order

There are four envelopes and corresponding $4$ letters.If the letters are placed in the envelopes at random,what is the probability that all the letters are not placed in the right envelopes? ...
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1answer
31 views

Mapping permutations to an index

I'm trying to calculate the distance-table (#of states as a function of the distance) of the 15-puzzle (has been done before in 2005 on a supercomputer by Korf et al.). There are $16!$ different ...
5
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1answer
63 views

Filling in blanks in a multiplication problem knowing only the set of digits in the product and that 9 divides each factor

The 5774 Ulpaniada (part 2 of it) includes the following question: The following multiplication exercises uses all $9$ digits $1,2,3,\ldots,9$. The digits are encoded by asterisks. We are told ...
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2answers
34 views

Permutations versus combinations, order or unordered (problem submitted).

A tourist wants to visit six of America’s ten largest cities. In how many ways can she do this if the order of her visits is (a) important, (b) not important? For part (a), I believe the answer is a ...
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2answers
97 views

How many $7$ digits number can be made?

How many $7$ digits number can be made with $1,2,3,4,5,6,7$ so that they are divisible by $11$? (Repetition is not allowed.) I know the divisibility rule of $11$, so the main problem is counting.
2
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1answer
29 views

Combinatorics Question - Permutations while fixing cases

Here is the wording of my question: In how many ways can a class with 20 students (12 boys and 8 girls elect a class president, vice president, and secretary if each student is willing to serve in ...
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1answer
28 views

Clarification for this combinations/permutations problem?

I've been going through a list of poker hands and their descriptions, and then attempting to calculate their probabilities by first calculating the number of possible hands for the given hand. I ...
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1answer
146 views

Project Euler #453 confusion

So I decided to give a shot on the #453 project euler problem but there is something that confuses me with the numbers given. I decided to start by calculating the possible arrangements of 4 vertices ...
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1answer
43 views

Permuting “123456728905”

In how many ways can 123456728905be permuted such that, neither two 2's nor two 5's are adjacent to each other ? I'm really confused how to ensure those ...
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1answer
32 views

What is the maximum number of iterations before a sequence is repeated

$A = \{a,b,c,d,e\}$ $B = \{f,g,h\}$ $C = \{i,j\}$ $D = \{0,1,2,3,4,5,6\}$ Suppose a four-tuple is constructed by extracting one element from each set at each successive iteration. The stipulation ...
2
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2answers
57 views

Describing the pattern in which iterations make two, cyclic sets equal

$A = \{a,b,c,d,e\}$ $B = \{a,b,c\}$ $C = \{0,1,2,3,4,5,6\}$ The first few iterations are as follows: $1.$ $a,a,0$ $2.$ $b,b,1$ $3.$ $c,c,2$ $4.$ $d,a,4$ $5.$ $e,b,5$ $...$ I'm trying to ...
0
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1answer
19 views

Determine possible combinations/permutations for 5 values which can be empty or not

This related to a computer programming rule I'm working on. I have 5 values: t1 t2 t3 t4 t5 and each of these values can be empty or not. Whether each one is empty or not will change the result that ...