# Questions tagged [combinatorics]

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

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### Estimate the number unique elements in a finite sample space via a finite sample without replacement

I have a pool of $N$ items. I know that there are $c$ distinct types of items in $N$ and the distribution of the distinct types is uniform, i.e. if I sample 1 item from the pool its chance of ...
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### Algorithms for solving combinatorial complexity problems in machine learning?

Many machine learning problems have combinatorial complexity. For example, in part-of-speech (POS) tagging in NLP, the goal is to predict one of possible $T$ tags for every word in a sentence of ...
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### What is the probability for an N-char string to appear in an M-length random string?

Link shortening service bit.ly allows you to, as you might expect, shorten URLs. URLs get shortened using a 7-character string. The alphabet of this string consists of a-z, A-Z and 0-9. Today, Dutch ...
34 views

### What is wrong with this self-made array shuffling algorithm? [duplicate]

I'm aware of the established array-shuffling algorithms, such as Knuth-Fisher-Yates. I'm interested in proving (or disproving) that my self-made shuffling algorithm is broken. It seems to be the ...
126 views

### Covariance matrix of combinations of independent normal distributions

I have a basket $X$ of items to choose from. Each $x_i$ is a normally distributed random variable $x_i \sim\mathcal{N}(\mu_i, \sigma_i^2)$. Each $x_i$ is independent and uncorrelated from every other ...
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### Probability of n columns of an array being identical

I'm trying to calculate the probability that p (or more) columns, of an n x m matrix, each ...
114 views

### Distribution like hypergeometric distribution, but with false replacements

I'm trying to find probabilities for a scenario that works exactly like hypergeometric distribution, except that every time you make a draw, you replace it with a "failure"-object. So eventually you'd ...
933 views

### How is the exact permutation test procedure carried out: iterating over permutations or using combinations of one group?

I've tried to find an article that explains the procedure of permutation tests for the exhaustive sampling of all permutations (not the monte carlo method) and couldn't find a resource that was ...
231 views

### Conditional combinations and permutations to identify sequences and patterns in R

I want to identify repeated behavioural patterns in a trader's account. The trader will typically transfer funds into his account denominated in a particular asset, buy and sell different assets, then ...
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### How many possible combinations of this stage given its a n * n grid?

Lets say you have n x n grid, and each square on the grid is either black or white. How many different combinations of this grid can exist? I figured 9! would be for the grid, but I don't know how to ...
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### all combinations of a vector of probabilities

I'm sure this is a simple problem, but I haven't been able to get to the bottom of it. I have a vector of probabilities, e.g. (P1, P2, P3). I'm trying to get the probability of each combination, e.g. ...
50 views

### Is there a closed form for sum of chooses?

Is there a closed form for $\sum_{i=a}^{b}\frac{{{i} \choose{n}}^2}{i}$?
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### How do you measure how “typical” a set of events are?

Given a set of events and their probability of occuring, where they all add to 1. Edit: the set of events can be of any size, the example below is only A and B with 50/50 probabilities for simplicity ...
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### Total number of ways 10 books can be arranged if 4 specific books may not be together?

I am trying to solve this albeit probably juvenile combination/permutation type question. A person has 10 books, of which four are fiction books. How many ways can the 10 books be arranged so that ...
88 views

### Probability of 0% correct choices [duplicate]

If I have 12 boxes, in order of #1 to #12, and I close my eyes and stick a known label (A to L) on a random box, what is the probability that I get zero correct labels on the corresponding boxes? In ...
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### Combination/Permutation Dilemma

This is probably quite a straight forward one - but still struggling to get my head around it. To explain my problem: In my work, I'm trying to put subjects into groups of 4 for a second round of an ...
76 views

### What's wrong with probability/combinatorics solution?

I was playing a game of cards with some friends and wondered : What's the probability of drawing 4 cards from a normal 52 card deck with all different ranks? I figured out 3 ways of achieving the ...
581 views

### Computing number of people with the same name and date of birth based on sample data

A country has a population of 40 000 000 people. I have a sample with data for 1 500 000 people from this country. In this sample 1.9% of people have a "pair" (one or more) with the same first name, ...
128 views