# Tagged Questions

For questions about the study of finite or countable discrete structures, specifically 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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### There are 4 nickle coins and 4 half nickle coins. How many different options are there for the sum of 5 coins.

I have this exercise in combinatorics: In a drawer there are 4 nickle coins and 4 half nickle coins, bob takes out from the drawer 5 nickles, how many different options are there for the sum of ...
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### Solutions to $a_1+2a_2+\cdots+ka_k = 1979$

For $k = 1,2,\ldots$ consider the $k$-tuples $(a_1,a_2,\ldots,a_k)$ of positive integers such that $$a_1+2a_2+\cdots+ka_k = 1979.$$ Show that there are as many such $k$-tuples with odd $k$ as there ...
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### How many ways are there to add up odd integers to 20?

How many ways are there to add up odd integers to 20? Here, $1+19$ is one solution, $19+1$ is a different solution, and $1+1+\dots+1$ counts as just one solution.
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### Number of ways to arrange $8$ rooks on a chessboard

Find the number of ways to arrange $8$ rooks on a chessboard such that no two of them attack other? I was thinking it would be $64 \times 49 \times 36 \times 25 \times 16 \times 9\times 4 \times 1$, ...