0
votes
1answer
53 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 ...
0
votes
0answers
26 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 $n$ ...
0
votes
1answer
27 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 ...
2
votes
2answers
52 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 ...
6
votes
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 ...
1
vote
3answers
43 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 ...
9
votes
3answers
118 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} ...
-1
votes
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
votes
0answers
69 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
votes
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 ...
1
vote
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?
1
vote
5answers
61 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?
0
votes
1answer
56 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 ...
0
votes
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
votes
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, ...
0
votes
0answers
53 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 ...
1
vote
2answers
74 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
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 ...
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
37 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
40 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
votes
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: ...
1
vote
1answer
39 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
vote
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 ...
0
votes
1answer
32 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 ...
-1
votes
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 ?
-2
votes
3answers
52 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
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 ...
2
votes
2answers
83 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
vote
3answers
54 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
84 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
95 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
1answer
77 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 ...
0
votes
0answers
31 views

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 ...
1
vote
2answers
20 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
33 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 ...
1
vote
0answers
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 ...
1
vote
1answer
45 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. ...
0
votes
1answer
64 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 ...
3
votes
1answer
35 views

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 ...
-1
votes
2answers
35 views

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 ...
2
votes
1answer
34 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 ...
3
votes
2answers
36 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 ...
0
votes
1answer
33 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 ...
0
votes
1answer
54 views

How many nonnegative integer matrices of size $N$ have all row and column sums equal to $D$?

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 ...
0
votes
1answer
24 views

Simple Permutations/Combinations Question

A group of 5 men and 5 women stand in line to have their photo taken. How many ways can they stand in line if no two men and no two women stand together? My method: _M_M_M_M_M_ Male * Female = 5P5 ...
2
votes
4answers
154 views

Permutation, Combinatorics

Stuck here : there are 100 objects labeled 1, 2,...100. They are arranged in all possible ways. How many arrangements are there in which object 28 comes before object 29. My approach : Consider ...
0
votes
0answers
34 views

Relation between permutations and fourier transform?

i dont know if this is already addressed somewhere (searching around did not find sth). The motivation is to find a way to generate or produce permutations using concepts from continuous mathematics ...
0
votes
1answer
21 views

Conjugating a permutation

I am trying to see that two permutations are conjugate exactly when they have the same cycle decomposition. I fail to see that $$r(i_1,i_2,\dots,i_k)r^{−1}=(r(i_1),r(i_2),\dots,r(i_k))$$ Any thoughts ...