Questions tagged [combinatorics]

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

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Ordered combinations

I have a combinatorics question. Say you have two sequences: $$X_{1},X_{2},X_{3},\ldots,X_{N_{1}}$$ and $$Y_{1},Y_{2},Y_{3},\ldots,Y_{N_{2}}$$ How can i pair up elements from the $X$'s with ...
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Probability of independent events within a specified window

So I have an event that can occur on a daily basis with probabilty 1%. There is no dependence between days. Now I can calculate the probabality of the event occuring X times in Y days: ...
870 views

Calculating possible combinations with restrictions

I have five additives that can be mixed into a chemical. Each one can be mixed in at a discrete percentage from 0.02% to 0.22% of the chemical (i.e. 0.02%, 0.03%, 0.04%,...0.22%). Each additive must ...
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Sampling with replacement

Suppose you have 40 different books (20 math books, 15 history books, and 5 geography books). Let M = math books, H = history books, G = geography books You pick 5 books at random, with replacement, ...
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What is the average expectation value of two specific objects in a queue?

I need some hand to solve this problem. Suppose a queue can be filled by three type objects (M, F and A). Depending on the number of each objects the line length can be different. We are looking ...
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Generating all possible unique combinations of dataset with two variables

I am fairly new to R and I have been reading all related topics but still I don't manage to solve my rather simple problem. I have a dataset with 5 cases for two variables (X,Y), for instance: ...
694 views

Probability of at least one unique outcome

We have n actors. Each actor chooses from n*2 actions. How can I calculate the probability that at least one actor will choose a unique outcome? For example, say we have 5 pickup artists in a town ...
601 views

The probability for two people to provide identical answers on survey questions

Here is the problem: A survey contains 7 binary questions (Yes/No responses). If two people are answering the survey, what is the probability for their answers on 4 or more of the questions to match? ...
877 views

Random permutation of a vector with a fixed expected sample correlation to the original?

Suppose you have an $n$-vector $X$. For a fixed real number, $r$ between $-1$ and $1$, can one generate a random permutation of the integers $1,2,\ldots,n$, call it $i_1,i_2,\ldots,i_n$ such that the ...
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What is wrong with this “naive” shuffling algorithm?

This is a follow-up to a Stackoverflow question about shuffling an array randomly. There are established algorithms (such as the Knuth-Fisher-Yates Shuffle) that one should use to shuffle an array, ...
10k views

Extending the birthday paradox to more than 2 people

In the traditional Birthday Paradox the question is "what are the chances that two or more people in a group of $n$ people share a birthday". I'm stuck on a problem which is an extension of this. ...