# 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.

38,016 questions
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### What is the difference between these two combinatorics problems?

So the first problem is "In how many ways can we arrange the letters in the word Alabama." and the second questions is "In how many ways can we arrange three Mathematics books, five English ...
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### Intuition on $\sum_{k=0}^{n}\binom{k+1}{k} = \binom{n + 2}{n}$

Intuition on $\sum_{k=0}^{n}\binom{k+1}{k} = \binom{n + 2}{n}$ I'm trying to understand what both sides count and why this equality holds. If the right hand side counts the number of binary strings ...
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### How many ways to tile a $2 \times N$ ring using $1 \times1$ and $1 \times 2$ tiles with different colors

Suppose we have a closed ring with size $2 \times N$, which is created by joining both ends (short edges) of a $2 \times N$ grid together without twisting. We have as many $1 \times1$ and $1 \times 2$ ...
### Choosing $r$ things from a set containing $l$ things of one kind, $m$ things of a different kind, $n$ things of a third kind,…
Here is a statement from a textbook that I'm referring to: From a set containing $l$ things of one kind, $m$ things of a different kind, $n$ things of a third kind and so on, the number of ways of ...