0
votes
0answers
45 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
69 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
27 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
0answers
17 views

To determine number of times male and females members of 2 family are arranged alternately in a row [on hold]

To arrange male and female (M,F) of 2 families denoted by P,Q and R,S respectively in such a way that there is exactly one flip (flip means PQ or QP together) in one family and considering the case of ...
0
votes
1answer
17 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
38 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
36 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
37 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
26 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
31 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
64 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
50 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
21 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
80 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
52 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
70 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
76 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
74 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
29 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
votes
0answers
58 views

Sum of possible permutations

Lets 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
32 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
82 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
43 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
55 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
33 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
32 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
35 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
23 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
153 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 ...
1
vote
0answers
31 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
20 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 ...
0
votes
4answers
29 views

Total number of unique permutations in a lexicographic set

Given N digits that can form a set, how many total unique permutations of the set can be generated if we do not care about the order of the digits in the set? Specifically, I'd like to ask for ...
4
votes
2answers
100 views

Count Number of Sequences

The question is: Given a sequence of positive integers A={1,2,3,...,N}. Count the number of sequences you can get after making K swaps between adjacent element on it for a given N ? My approach: My ...
2
votes
3answers
61 views

Why is the number of arrangements of $n$ objects equal to $n!$?

I hope this question does not seem vague, but whats the logic/reason behind that e.g. One can arrange 5 colours in $5!$ different ways if all of the colours are different?
2
votes
0answers
206 views

Count swap permutations

Given an array A = [1, 2, 3, ..., n]: ...
0
votes
3answers
32 views

DNA Sequence Distinct Way

we know The genetic code is based on the four nucleotides adenine (A), cytosine (C), guanine (G), and thymine (T). These are connected in long strings to form DNA molecule. with three A, one C, two G ...
2
votes
2answers
50 views

how many ways 3 pairs can be selected out of 6 students?

Out of "6 students" how many ways can 3 pairs be selected for assigning homework ?
2
votes
0answers
35 views

Possible number of permutations

I've generally been seeing the formula nPr = n!/(n-r)! to calculate the number of permutations. But this is the case only when elements cannot be repeated, am I correct? If elements can be repeated, ...
1
vote
0answers
35 views

How many different sequences in this event?

There are $10$ students in the class. Four of these students will be selected randomly to participate in the math contest. Then, how many different sequences can four students be selected? I thought ...
1
vote
2answers
28 views

Find the number of different teams that can be selected if the team contains all $4$ women?

A team of $6$ people is to be selected from $8$ men and $4$ women. Find the number of different teams that can be selected if: (i) there are no restrictions, (I solved this using ${n\choose ...
0
votes
2answers
41 views

Find how many of these $4$-digit numbers are even. [closed]

(a) (i) Find how many different $4$-digit numbers can be formed from the digits $1, 3, 5, 6, 8$ and $9$ if each digit may be used only once. I did this; the answer is $360$; I used ...
1
vote
0answers
58 views

password attempts

The password must have a length of 8 and be composed of lower case letters and/or numbers (letters and numbers can be repeated). Suppose someone wants to access your online bank account. ...
0
votes
1answer
25 views

number of possible combinations of events

I am not a mathematician but I'm giving a lecture on the scope of a number of people in a given group to interact. There are 40 people in an affinity group Each person has 10 unique items of ...
2
votes
3answers
36 views

Permutations with repetitions - which is k and which is n?

I am learning permutations with repetitions, and working with the formula that $P(n,k)=n^k$. I understand the logic that with repetitions, we multiply $n$ by itself $k$ times. But in different ...
0
votes
1answer
29 views

probability of finding a small sequence within a larger sequence

I'm wondering how to define the probability of a long string LS (using 26 letters alphabet) to contain a smaller string ss. Right know I have something like this. Number of LS containing ss: 26^( ...