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

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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 ...
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43 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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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 ...
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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 ...
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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 ...
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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 ...
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2answers
75 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 ...
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1answer
29 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 ...
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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 ...
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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 ...
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1answer
41 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 ...
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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. ...
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1answer
40 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: ...
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0answers
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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 ...
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1answer
39 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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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 $A_n$ ...
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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, ...
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2answers
34 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
40 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 ...
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1answer
27 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 ...
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1answer
33 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
67 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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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 $12$ ?
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1answer
23 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 ...
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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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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 ...
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2answers
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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 ...
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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
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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 ...
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1answer
86 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 ...
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2answers
96 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 ...
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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 ...
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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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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
22 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 ...
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1answer
14 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 ...
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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 ...
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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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1answer
82 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
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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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2answers
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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
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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
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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
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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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87 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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1answer
37 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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1answer
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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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1answer
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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.