# Questions tagged [combinatorics]

Counting or enumerating elements in a set or other finite discrete structure.

294 questions
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### I need to know how many combinations are possible from these, if I must select at least one (but can choose more than one) from each table

I have a very simple permutation question that I can't figure out on my own. So, I have {A, B, C} and {D, E, F} I need to ...
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### Formulaic way to calculate the numerator of a probability mass function?

Problem description A package contains six batteries. Two of them are defective. Suppose that we randomly select three batteries and test them for defects. What is the probability that ...
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I have 5 Americans, 4 Mexicans, 3 Argentines and 2 Uruguayans. If I want to form a committee of 5 people, with the condition that each nationality is represented I know that I have to calculate the ...
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### How many ways there are to add up 7 numbers to sum of 180?

Farmer has 7 pigs and 180 potatoes. How many combinations of distributing those 180 potatoes there are? Order does not matter. Each pig can get from zero to 180 potatoes, but all 7 pigs must get ...
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### Finding optimal correspondences between objects given two square distance matrices

I would like to find the optimal correspondences between two systems of objects based on the distances between objects WITHIN the two systems. So, the input to the algorithm would be two square ...
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### Rearrange 2D grid [closed]

I have a 2D grid on which I represent data points: Here, the red data point activates the grid on positions (1,1), (1,4) and (2,3). The blue data point activates the grid on positions (1,1), (4,3), (...
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### How many combinations of K ordered numbers from N numbers list

I have N numbers, 1-N (my N is 70). I need to know how many combinations of sequences of K numbers (K is 8 in my case) are possible, where the sequence is always increasing. Examples: 1,6,23,45,51,...
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### 10 cards out - chance of 2 aces out

Poker - 52 cards 4 suits of 13 cards each A deck will have 4 aces Let say 5 player - 10 cards pre flop Poker probability What is the chance exactly 2 aces are out (in the 10 cards dealt)? Is ...
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### Ways to make a straight in poker

A deck is 4 suits of 13 cards each. The ace is both low and high so that is why you have 10 ways to make a straight. A flush is all cards of the same suite. There are two hands (flush and full house)...
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### Looking for canonical problems or seminal work it the intersection of constraint programming and statistics

I'm interested in exploring the area (if it exists) at the intersection of constraint programming and statistics. My primary interest is on problems that require a combination of both statistical and ...
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### Relationship between CLT for estimator of sample and number of combinations for subsample?

What is the relationship between the Central Limit Theorem as applied to the expected value of an estimator of a parent sample and the number of possible combinations of a subsample used to calculate ...
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### Sampling combinations

I'm running a simulation where the different inputs are combinations of $n$ values taken in $r$. The problem is that even though $n$ is small, the number of different combinations is very large, so I ...
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### Show that a random variable is distributed as a Geometric rv

I am working on an assignment: I have a line of numbers that is divided in intervals of fixed length, so for example: [0,c), [c,2c), [2c,3c), etc. Each interval is numbered 1,2,3 etc. X is an ...
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### Unique vectors that can result from bootstrapping

My question concerns the unique number of vectors that can result from bootstrapping. Ie I have a vector of length 12 with the following elements : 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1 and I would like to ...