# Questions tagged [combinatorics]

For questions about the study of finite or countable discrete structures, especially how to count or enumerate elements in a set (perhaps of all possibilities) or any subset. It includes questions on permutations, combinations, bijective proofs, and generating functions.

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### Distribution of items among two people, from PSS by Arthur Engel.

The following question is from Arthur Engel's Problem-Solving Strategies: $2n$ objects each of three kinds are given to two persons, so that each person gets $3n$ objects. Prove that this can be done ...
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### Find number of matrices $B$ with no common row and no common column with a given matrix $A$

We are given a matrix $A$ with $n$ rows and $n$ columns and it's elements are $1,2,...,n^2$ (each element appears once). Find the number of matrices $B$ whose elements are $1,2,...,n^2$ that does not ...
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### How many digits in the sequence 1,2,4,8,16,…,2^150? [closed]

I know how to calculate number of digits if the sequence is linear growth, for exmaple, 3,6,9,...,3333 3,6,9 --> 1*3 = 3 digit 12,...,99 --> 2*((99-12)/3+1) = 60 digit 102,...,999 --> 3*((999-102)/...
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### Probability that exactly $r$ tables are occupied if $k$ people randomly select a table

There are $n$ tables with infinite capacity. Each of the $k$ guests randomly (with uniform distribution) and independently select a table to sit next to. What is the probability that exactly $r$ ...
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### Incorrect combinatorics reasoning

There are $5$ cows, $8$ roosters, and $10$ pigs on a farm. The farmer wants to pick $4$ animals, and at least $1$ needs to be a cow. He asked his (alleged) prodigious son Smarty how many ways it can ...
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### Arranging the $26$ English letters in a row given two constraints

In how many ways can we arrange the $26$ English letters in a row so that no two vowels are adjacent to each other, and each block of consonant(s) (between $2$ vowels) is/are in alphabetical order?...
Given a vector space with tensor structure $V\otimes V\otimes V....\otimes V$, it is naturally (at least for us people doing many-body physics) to think that its subspaces are also equipped with some ...