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

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3
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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
44 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) $504$
1
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1answer
299 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
votes
1answer
107 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
65 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
votes
1answer
56 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 ? ...
5
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3answers
83 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 ...
0
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3answers
52 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
46 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
60 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
57 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
46 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 ...
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2answers
56 views

Probability query

8 Indians and 3 Americans are to stand in a row at random. What is the probability that no 2 Americans are always together? I think the answer should be 1 because as there are many possible ...
1
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2answers
83 views

Number of possible patterns?

Using the following rule: Each column and each row must contain at least one point, how many patterns can a 4x4 grid (thus with 16 possible point positions) generate? (this rule would thus make the ...
0
votes
1answer
44 views

To calculate number of combination of sequences having 1 and 2 alternating sequences of R and S.

I have a sequence of 6 letters containing 2 P, 2 R , 1 Q and 1 S. I have PPQ, now I have to add two R and one S in that, these can be placed anywhere. There will be total 60 possible ways to do that ...
0
votes
1answer
18 views

Distribution combinations

How many ways can 25 identical pencils be distributed between two people?.Each all pencils must be shared out. A) Each person must have at least 5 pencils? B) Each person must have at least 7 ...
1
vote
1answer
39 views

paths from from point A to point B with length 8

Question How many paths from point A to point B with length 8 exists that that have even number of negative signs? path example my main problem is that i can't find a good way for counting ...
0
votes
1answer
42 views

prove $a^2_o-a^2_1+a^2_2-…+(-1)^{n-1}a^2_{n-1}=\frac {1}{2}(a_n+(-1)^{n+1}a^2_n)$

Question if $a_k$ is multinomial coefficient of $x^k$ in polynomial $(1+x+x^2)^n$,where $0\le k\le 2n$,prove: using this equality $(1+x+x^2)(1-x+x^2)=1+x^2+x^4$,show that ...
0
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2answers
32 views

Ways to award first and second place to two persons out of nine

Question: In how many ways can the first and second place be awarded to two persons from among 9 people. ...
0
votes
1answer
54 views

About permutation with repeated identical elements.

First up, I do know the general solution but somehow am unable to use it to solve this kind of problem. I am simply lost. The problem is like this: ...
2
votes
0answers
55 views

What do you call the following operations on a symmetric matrix?

Suppose we have a symmetric matrix of the following form, where the diagonal is always zero: \begin{array}{cccc} 0 & 1 & 1 & 0\\ 1 & 0 & 1 & 1\\ 1 & 1 & 0 & 0\\ 0 ...
1
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1answer
57 views

Prove by Structural induction, circular permutations

Prove by Structural Induction: For a circular permutation of $n$ elements, the number of permutations is $(n-1)!$ How is this done?
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0answers
18 views

Bijection from permutations to restricted n-tuples

Let $A_n$ be the set of permutations of $1,\dots,n$. Let $B_n$ be the set of $n$-tuples $(b_1,\dots,b_n)$ such that $1\le b_i\le i$ for each $i\in 1,\dots, n$. Construct a bijection from $A_n$ ...
0
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0answers
34 views

Signing the attendance

Imagine N students sitting in a straight row, students are numbered 1 to N. Attendance sheet is first given to student 1, who uses his own pen to sign the sheet. Then he passes the sheet to student 2, ...
2
votes
2answers
47 views

Possible ways of 8 digit numbers using 1,2 and 3 such that the number has atleast one digit for each 1,2,and 3

How many 8 digit numbers can be formed using the digits 1,2 and 3 so that the number contains at least one of each of these three digits?
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1answer
45 views

Counting squares in a given k by k square..

So the question is : The solution to this problem according to the book is to first count the number of squares whose sides are parallel to the sides of this 10 by 10 square and then to count the ...
1
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1answer
28 views

permutations with a given condition!

What will be the number of permutations of n different things, taken r at a time,when p particular things is to be always included in each arrangement? I know the answer to this question but could not ...
0
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1answer
34 views

The number of ways of going up 7 steps …

The number of ways of going up 7 steps if we take one or two steps at a time is ? So its essentially asking in how many ways can we make use of numbers of (1,2) to get a sum of 7. Am I wrong up till ...
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3answers
72 views

In how many ways can you choose three distinct numbers … [closed]

In how many ways can you choose three distinct numbers from the set of {1,2,3,...,19,20} such that their product is divisible by 4 ?
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3answers
58 views

How many digits… [closed]

How many $3$ digit numbers of distinct digits can be formed by using the digits $1,2,3,4,5,9$ such that the sum of the digits is at least $12$ ?
1
vote
1answer
27 views

Number of arrangement

Problem: What is the formula of number of arrangements? More specifically I need to avoid repeated elements and the order of the sequence does not matter. For lucidity I show an example: For 3 ...
0
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1answer
9 views

permutation game labels

A computer game has five difficulty levels. In each level you can choose among four different scenarios except for the first level, where you can choose among three scenarios only. How many ...
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0answers
36 views

Color Cyclic Permutations

Suppose there are n people sitting in a circle,wearing 3 kind of shirts viz. white,red and green. When two people with different shirt color talk with each other, they both change their shirt to ...
2
votes
2answers
92 views

A simple question in combinatorics.

A university bus stops at some terminal where one professor,one student and one clerk has to ride on bus.There are six empty seats.How many possible combinations of seating? My problem:I know that if ...
1
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0answers
58 views

Arrangement of 4 boys and 4 girls with no two girls are next to each other?

Let we have 4 boys and 4 girls and we need to arrange them, with no two boys and no two girls are next to each other? Let place first the boys b b b b the 4 ...
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3answers
56 views

Question regarding permutations and combinations?

Hi, I was just wondering on how you are supposed to approach this question. I keep getting 114 as an answer, but the answers say it is 174. How would anyone do this question, because I feel like I'm ...
3
votes
1answer
110 views

Counting possible combinations to open a lock( 2006 ACM ICPC)

I was working on a problem in a coding competition and I began to wonder about the analytical (mathematical) solution to this problem. I am not even sure how to go about counting this. Any ideas will ...
0
votes
2answers
101 views

please help me ( probabilities )

please let me know if my answer true or false Three numbers are chosen at random without replacement from the set {0, 1, 2, 3, ... , 10}. Calculate the probabilities that for the three numbers drawn ...
0
votes
2answers
15 views

Permutation of objects selected from a group

I'm having trouble with this question: How many numbers greater than 300 can be formed from the figures 4, 3, 2 and 1 if each figure can be used no more than once in each number and all the ...
0
votes
1answer
78 views

How to find out the number of ways to solve Instant Insanity

Problem : We are given 4 cubes. The 6 faces of every cube are variously colored - Blue, Green, Red or White. Stack the cubes on top of another in such a way that no color appears twice on any of the ...
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0answers
20 views

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 ...
1
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1answer
29 views

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 ...
1
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1answer
15 views

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 ...
0
votes
1answer
17 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 ...
2
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0answers
81 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 ...
2
votes
1answer
85 views

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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1answer
41 views

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 ...
1
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2answers
22 views

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 ...
1
vote
3answers
36 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 ...
1
vote
3answers
73 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 ...