# Questions tagged [combinatorics]

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

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### Use sum of p-values from significance tests to determine best permutation of table columns

I have a table in which there are columns which are entirely filled with numbers. Given another table, I want to figure out which permutation of the other table's columns produces an arrangement most ...
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### How would you work out the total number of possible plays in a game of dominoes?

Looking at a standard double-six dominoes set that has 28 tiles 0:0 through 6:6 how would we calculate (or estimate) the number of possible moves in a single game? For this so far I've come up with: ...
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### Amount of Possible Bootstrap Samples

I know that the total possible amount of distinct bootstrap resamples of size $n$ is $\binom{2n-1}{n-1}$. Is there any way to prove or justify this?
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### Closed form of pairing probability

This situation happened to me at home today, and now it is bugging me. I didn't put all my clothes in the washing machine, and I retrieved 7 sockets, 2 pairs of socks and 3 unpaired ones. I wanted to ...
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### Probability of x out of G objects sharing a bucket with the R randomly distributed other objects in n buckets? [closed]

If I have n buckets, and there are G green balls randomly put in those buckets, one at a time, and I put R red balls randomly, also one at a time, in those n buckets, what is the formula for the ...
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### Drawing from 2 bags of different size and counting the number of outcomes

I have a combination problem that I can't get my head around. Similar problems were found here and here but are not quite the same of my problem. I have two sets of units and I want to find the ...
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### Combinatory probability, group composed by different balls of different colors

Let's say you have a group of $M$ balls of different colors in a box. For example, 20 balls are red, 15 are blue, 10 are green, 5 are grey, 5 are yellow and 5 violet, for a total of $M=60$ balls. ...
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### Combinatorial explanation for $2n$th moment of standard normal distribution?

The $2n^\text{th}$ moment of the standard normal distribution $X \sim \text{N}(0, 1)$ is given by: $$\mathbb{E}(X^{2n}) = \frac{(2n)!}{2^n n!},$$ which is also the number of ways to divide $2n$ ...
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### Difficulty Understanding Application of the Multiplication Principle

While leafing through "Introduction to Probability" (Hwang, Blitzstein), I encountered the following problem. A standard deck of cards is shuffled well. Two cards are drawn randomly, one at ...
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