Combinations are subsets of a given size of a given finite set. All questions for this tag have to directly involve combinations; if instead the question is about binomial coefficients, use that tag.

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2
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1answer
14 views

How to find the N-th 3 word sequence within the following constraints

I have a list of words. Let's say that I have an algorithm(explained below) to generate the permutations in a specific order. I want to be able to find the N-th permutation easily. I want to make ...
-6
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1answer
31 views

Finding the number of possible shortest ways.

Find the number of possible shortest ways from A to B.
0
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0answers
22 views

What is the minimum number of vertices needed to create n non-overlapping triangles

How can I calculate the minimum number of vertices needed to draw $n$ non-overlapping triangles? Details There is no restraint on collinearity of the vertices. I don't think $^nC_3$ is correct (...
1
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0answers
32 views

combination problem on Lego blocks

Working on some interesting combination problems related to Lego blocks. For example, this one. Confusion is, I often see two dimensions (e.g. height and width in below problem) mentioned to calculate ...
1
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2answers
49 views
3
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3answers
94 views

Number of positive unequal integer solutions of $x+y+z+w=20$

What is the number of positive different integer solutions of $x+y+z+w=20$, where $x,y,z,w$ are all different and positive? It would be nice if coding is not used. I am given the answer $552$.
1
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1answer
25 views

Betting ended after nth round.Find the sum of money NOT WON?

Rahul and Vijay are playing a game with 12-sided die,where both of them lay bets on outcomes of roll of die.They start betting Rs 5 each on first round of the game and the amount bet in each ...
1
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5answers
60 views

Arrange black and white balls so that each pair of white balls is separated by at least two black balls

I am trying to solve the following question: How many linear arrangements of $m$ white balls and $(n-m)$ black balls are possible such that each pair of white balls is separated by at least two ...
3
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1answer
31 views

Generic method to distribute n distinct objects among r people such that each person gets at least one object

Is there any generic method to solve problems of the kind - "How many ways to distribute n distinct objects among r person(s) such that each person gets at least 1 object?". I am aware of 2 different ...
0
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1answer
20 views

N objects among K persons

In how many ways can we distribute N objects among K people such that each person recieves AT LEAST ONE object ? Also the SUM MUST BE EQUAL TO N. eg. 7 objects can be distributed among 5 people in 2 ...
3
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0answers
30 views

Sum of combinations with duplicates

In a bag I have: Five 10c coins Two 25c coins If I pick out three coins from the bag. What are all the possible amounts of money I could have. The answer is: 30c (3x10c coins), 45c (1x25c ...
0
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0answers
31 views

would it be possible to measure neural network combination/ representation as capacity?

My question is about machine learning, If you are familiar with you the restricted Bolatzmanne machine. I would like to know if we can implements some ideas. RBM in simpler case is just two layers ...
1
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0answers
65 views

How many possible solutions are there in 4 number game?

$4$ number game consist of $4$ random number from $0$ to $9$. The goal is to make the result equal to $24$. There are only operation four operation possible, addition, subtraction, multiplication, and ...
0
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1answer
21 views

Permutation/Combination Assistance

I'm stuck on the following permutation/combination problem... John won 10 tickets to the Falcons/Ravens game by calling into a radio station’s contest. Find the number of ways he can invite family ...
-1
votes
3answers
100 views

number of possible combinations of 5 from the set of numbers 1-10

I am trying to figure out how to set up this problem or any similar one. If you have 10 balls numbered from 1 to 10, and you pick 5 balls, what is the probability that you will have picked ball#1? In ...
2
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4answers
53 views

Circular Arrangement with numbers

The number of ways of arranging 2 women and 7 men around a circular table containing nine numbered chairs such that the women are not together. I am getting answer as 7!*7c2(arranging 2 women in the ...
0
votes
2answers
56 views

A soccer squad contains $3$ goalkeepers, $7$ defenders, $9$ midfielders and $4$ forwards.

A soccer squad contains $3$ goalkeepers, $7$ defenders, $9$ midfielders and $4$ forwards. So I understood the first part of the question: $(i)$ In how many ways can a team of $1$ goalkeeper, $4$ ...
0
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0answers
20 views

minimum distance of a linear codes

My question is about computing the minimum distance (weight) of a linear code. Assume that we have the generating matrix of the code. Then we can easily compute the weights of each row and of course ...
1
vote
1answer
30 views

Trying to find the rank of the word permutation .

What is the rank of the word $PERMUTATION$ if all the words formed by the letters of "$PERMUTATION$" are arranged in ascending order ? $PERMUTATION$ in ascending order in $\{A,E,I,M,N,O,P,R,T,T,U\}$ ...
1
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1answer
25 views

Solving for possible orientations of 3 objects on a 3x3 grid [closed]

Say you have a 3x3 grid, and 3 objects to work with. Each occupies one space. How would I go about solving the amount of ways they can lay on the grid. Example: (pardon my bad ASCII art) [][][] [][][]...
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0answers
23 views

Is this statement permutation or combination? [closed]

How many ways can a person select five different numbers between 1 and 14 (inclusive)? (1 mark)
2
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1answer
45 views

In how many ways can these people be arranged for a photograph?

Jessie and Casey are getting married. In how many ways can a photographer at their wedding arrange 6 people in a row from a group of 10 people, where the spouses are among these 10 people, if both ...
0
votes
3answers
46 views

Number of ways to select men and women to a committee?

A committee to contain $5$ members and have at least one woman. There are $7$ women and $9$ men. I think that we can fix one woman as one of the $5$ members, and randomly select the rest from a ...
0
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2answers
48 views

How many different arrangements of seating can my friends and I sit at the movies? [closed]

Myself and 6 of my friends (1,2,3,4,5 and 6) have organised to see a movie. I am about to give the seat tickets out to my friends. However my friends have a complex relationship with each other. 1 ...
1
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1answer
37 views

Probability of picking balls with same color with replacement and without replacement

This is one of our probability exercise: We have an urn with m green balls and n yellow balls. Two balls are drawn at random. What is the probability that the two balls have the same color? (...
0
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1answer
16 views

Formula for combinations number with aggregation

I've this scenario, 4 groups (as follow) with following values: Dimension A: A B Dimension B: K J L Dimension C: X Y Dimension D: F G I want to know numbers all possible combinations, ...
0
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1answer
24 views

Find $i^{\text{th}}k-\text{combination}$ in lexicographic order

I would like to obtain the $i^{\text{th}}k-\text{combination}$ in lexicographic order. For instance, for $comb(10,5)$: $i=0: [0,1,2,3,4]$ $i=1: [0,1,2,3,5]$ $i=2: [0,1,2,3,6]$ $\dots$ $i=10: [0,1,2,...
0
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0answers
21 views

Probability of getting a “full house” by rolling dice [duplicate]

In poker, full house means getting three cards with the same rank, and another two cards with the same rank (not the same as other three cards). I can understand how to use combination to solve this ...
2
votes
3answers
38 views

Multiple objects, Number of combinations

A bag contains colored balls: 8 red balls 4 white balls 4 blue balls 4 green balls 2 purple balls 2 orange balls 1 yellow ball 1 black ball Total of 26 balls. I'd like to determine the number of ...
2
votes
1answer
63 views

Derangement combination calculation

For the traditional classic problem of derangement (https://en.wikipedia.org/wiki/Derangement), there is a formula $n! = (n-1)(!(n-1)+!(n-2))$, which calculates current results based on previous ...
2
votes
1answer
22 views

Ordered Integral solutions

If $a\times b\times c = 12 \times \gcd(a,b,c)$, how many ordered triplets $(a,b,c)$ are possible? Assuming $a=hx,b=hy,c=hz$ where $h=\gcd(a,b,c)$ .I am getting $h^2xyz=12$. Solving this I am getting ...
1
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1answer
25 views

2 variables “variable weighting” function

I have two variables $X,Y \in [0,1]$ and want to output some kind of weighted indicator based on these two. X is a raw indicator value where a low value indicates good health, and Y measures ...
0
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3answers
34 views

A boat is to be manned by 8 men,of whom 2 can only row on bow side & 1 can only row on stroke side;in how many ways can the crew be arranged?

I tried it by selecting 2 men out of 8 for bow side,and then arrange them in 2! ways.This can be done in$ \binom{8}{2}$*2! ways,and the stroke side can be crewed in 6 ways.So the required no. of ways ...
0
votes
2answers
36 views

6 women, 7 men form a pair of 1 woman 1 man. How many ways can we select 3 pairs.

So the way to do this I think is to 6C3*7C3*9 (where 9 is the number of ways we can arrange the men and women within the 3 pairs). But I can't seem to figure out how I would do this in a different ...
2
votes
4answers
93 views

Number of positive unordered integral solutions

What are the number of positive unordered integral solutions for $a+b+c=36$ Solution given is $108.$.But I am getting $91$ as $$\frac{\binom{35}2-3\times16-1}{3!}.$$ $3\times16($ for $a=b$ cases and ...
2
votes
1answer
38 views

Combinatorics: Color a wall such that not two neighbored slots have the same color

We have a wall with $7$ slots. We can color the wall either with blue or red. How many combinations do we have to color the wall if two red slots cannot be neighbors? I thought, in a very intuitive ...
2
votes
2answers
26 views

Nr. of combinations given K stars and N borders

I am given K stars(X's) and N inner borders, in how many unique ways can I arrange them ? empty spaces between borders is allowed. Some examples: 0 inner borders and 3 stars => 1 combination (if no ...
0
votes
3answers
35 views

How many selections of four of six numbered balls involve selecting exactly one or two of the first three numbers?

In a box, there are $6$ balls, that can be distinguished (numbered from 1 to 6)! How many possibilities do we have, by taking $4$ balls (all at once) without considering the order to have exactly $1$ ...
0
votes
1answer
35 views

Calculating the odds of winning a game

Problem: You, the user have 3 lives. In front of you are 5 cups - in each cup there is a piece of paper with 1 random number between 1 and 5 (inclusive) written on it. You must guess the number in ...
3
votes
1answer
66 views

How many ways are there to pick a collection of 12 coins from piles of pennies, nickels, dimes, and quarters?

How many ways are there to pick a collection of 12 coins from piles of pennies, nickels, dimes, and quarters? a) Assuming that each pile has at least 12 or more coins. For this one, I got CR(4,12) =...
1
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0answers
22 views

Relation of relative numbers of (restricted) ways to distribute identical / distinct objects into distinct bins

If want to know if the following inequality holds for general values of $s \leq n \ll m$. $$\frac{C_0(n,m,s)}{C_0(n,m)} \leq \frac{p(n,m,s)}{m^n}$$ $C_0(n,m) = \binom{n+m-1}{m-1}$ is the number of ...
2
votes
1answer
28 views

creating a balanced gray code with digits of different parity

I have some code that generates all combinations from something like this: [the or a] and [angry or mad or furious] and [cat or feline] to this: ...
0
votes
1answer
19 views

Combination with Repetitions Including Duplication of N Value

Is a Combination with Repetition the correct term for the following problem N - Letters a, b, c R - 2 Example Result should equal aa ab ac bb ba bc cc ca cb Total ...
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0answers
20 views

Using combinatorial optimization to find the shortest route

My question is, given 5 locations all with (x, y) co-ordinates, how would I calculate the shortest route where each location is visited one time?
1
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1answer
36 views

Prove : Each distinct $R_{k,e}$ can appear maximum $\sqrt b \leq n^{3}$ times.

Notation: $H$ is the adjacency matrix of graph $H'$ respectively. $H_k$ is the block or sub-matrix of matrix $H$. The adjacency matrix of graph $H_k \cup H_e$ (subgraphs of $H'$) is $M_{(k,e)}$ ...
0
votes
2answers
17 views

Compute the $3$-Combinations for a $4$-digits set

Consider we have $4$ digits. We want to compute the $3$ digit combinations of these $4$ digits ($1-2-3-4$). From the formula, we have: $$\frac{n!}{k!(n-k)!} = \frac{4!}{3!1!} = 4$$ but when I try ...
1
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2answers
36 views

Are these two events in $S_{30}$ independent?

Let $S = S_{30}$, the set of permutations on $\{1,...,30\}$. Suppose $A$ is the event: $\{\pi\in S_{30}: \pi(1) = 1\}$ and $B$ is the event $\{\pi\in S_{30}: \pi(2) < \pi(3)\}$. I am asked to ...