-1
votes
0answers
36 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
16 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 ...
0
votes
3answers
25 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
68 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
78 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
42 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
45 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
30 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
32 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 ...
0
votes
0answers
29 views

Count number of repetitive customer visiting a restaurant [closed]

Suppose a restaurant at the end of year, come to know that he served 10800 Customers. What number or percentage of customers would be repetitive customers. Because all 10800 Can not be new customers. ...
2
votes
1answer
30 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
31 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
32 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
21 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
152 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
28 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
27 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
97 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
60 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
205 views

Count swap permutations

Given an array A = [1, 2, 3, ..., n]: ...
0
votes
3answers
29 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
47 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
34 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
27 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 ...
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. ...
-1
votes
0answers
175 views

Count number of subsequence that will form an Arithmatic Progression

Given a sequence X of integers between 1 and 100. The number of elements in sequence X may contain upto 105 elements. Find out how many number of subsequences will be there which are in arithmatic ...
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^( ...
1
vote
2answers
29 views

combinations and permutations - choosing when there's a limit

A kid can choose 7 out of 12 donuts to eat. How many ways can he do this if he must choose at exactly 3 of the first 5? Similarly, how many combinations are there if he must choose at least 3 of the ...
0
votes
2answers
27 views

Combinations and permutations when separating into groups

If I have 30 people and I want to form them into 3 groups. One of size 10, one of size 5 and one of size 15. How many ways can I do this? Similarly what if I have 15 boys and 15 girls and the 10 ...
0
votes
2answers
78 views

combination GRE problem 25

An appliance's model number consists of three alphanumeric characters. The first character must be one of 24 permissible letters of the alphabet. The next character is numeric, a digit from 1 to 9. ...
2
votes
0answers
38 views

Find k such that, $\displaystyle\frac{n^{\underline k}}{n^k}<a$

How to find k here $\displaystyle\frac{n^{\underline k}}{n^k}<a$ ? With, $n^{\underline k}=n\cdot(n-1)\cdot...(n-k+1)$ and $(n>k,\ a>0)$ Of course if $k\approx n/2$ the inequality ...
-5
votes
1answer
62 views

Dividing a set of n elements into k disjoint subsets.

I have been able to do the 1st part. I have not been able to prove the 2nd part. My attempt to the solution :- I took $k$ groups $ a_1, a_2, a_3…, a_k $ Let $a_1$ group has $b_1$ similarly so ...
0
votes
1answer
48 views

What is the meaning of nCk X nPk?

I am trying to understand the bulls and cows document, Page 6 , equivalences . Can someone please tell me what author means when he says nCk x nPk like 4P0 X 4C0 , 4P1 X 4C1 ?
0
votes
1answer
17 views

Given a string containing 'a' and 'b', Find all permutations starting with 'a'

Given a string contains only a and b where a comes M times and b comes N times in the string. I need to compute all the permutation of the string starting with a. What is the most efficient way? Can ...
0
votes
2answers
55 views

Probability: What is wrong with my approaches?

$4$ out of $20$ balls are black. The others are white. If I pick $2$ balls out of those $20$ randomly, what is the probability that at least one of them is white? I could do this using a ...
0
votes
0answers
33 views

Formula to generate combination of number series with a fixed sum

If I have number 65. So that x = 65, and 5 numbers were added to get this number 65, say 20 + 15 + 5 + 10 + 15 What I want to find out is this Is there a formula to generate all the possible sets of ...
0
votes
1answer
20 views

Ordered Partitions

I'm having trouble figuring out exactly how one would get the answer for a question such as: "how many ways can 9 concert tickets be divided between 4 concertgoers, such that one person receives 3 ...
0
votes
3answers
75 views

Probability: deep understanding of permutations and combinations.

Look at this problem: If one is to throw $2$ dice, what is the probability that he/she gets a total of exactly $4$ dots? Well, the amount of the events that satisfy the condition is $3$ as we ...
2
votes
2answers
18 views

What's the name of the minimum number of transpositions required to build a permutation?

What's the name of the minimum number of transpositions required to build a permutation? I thought it was "rank" but apparently "rank" refers to the lexicographic number.
3
votes
3answers
49 views

Conjugate to the Permutation

How many elements in $S_{12}$ are conjugate to the permutation $$\sigma=(6,2,4,8)(3,5,1)(10,11,7)(9,12)?$$ How many elements commute with $\sigma$ in $S_{12}$? I believe I use the equation ...
1
vote
1answer
52 views

How Many Permutations of Die Rolls Add Up to a Fixed Total?

I'm toying around with the idea of designing a board game. I like the idea of a hexagon-tile setup (a la Catan). There would be some number of different resource categories; I'm trying to determine ...
0
votes
2answers
25 views

Probability questions need help

1) You're going to a theme park with your family and they allow you to bring at least one but no more than 3 friends with you. If you choose from 8 friends, how many different grouping can be ...
1
vote
1answer
29 views

Number of ways of selection from a mixed group

For example I want to know number of ways I can select $2$ items from $AAABBC$ i,e $3$ of one group,$2$ of other and $1$ of last.
1
vote
1answer
48 views

Basic combinatorics question, can you help me?

Before I start let me thank anyone that contributes to helping me with an answer for this. Ok - on to the question. Assume you have 10 jelly beans, 5 yellow and 5 red. What is the total amount of ...
0
votes
1answer
16 views

Count the number of mixes of the card to get come back to origin

Mix a deck of 52 cards by placing them in two parts and take alternate cards from both stacks. Use the cycle notation to show that it only takes 8 mixes to come back to the origin. Since we want ...
0
votes
2answers
32 views

Calculating permutation of n items under pattern constraints

I am trying to find a formulae that gives the number of unique permutations of an arbitrary number of items, constrained with the following pattern: For every item X: X' must always appear at some ...