# 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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### Probability that the picked hand will have at least one sequence in a game of Rummy with two standard decks

QUESTION: The game of Rummy is usually played with two standard decks of cards each containing 52 cards.Both of the deck contain four suits -hearts(h), diamond(d),club(c) and spade(s) comprising of ...
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### Combinatorial Proof Question [on hold]

Combinatorial Proof Question I know I need to count strings with n entires, where each entry must lie in {0,1,2}. Just need further hint.
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### Paths from source to destination in directed bounded in-degree bipartite graphs?

Given $n$ vertex $m$ edge bipartite graph on condition that each vertex has in-degree at most $1$ (out-degree unbounded) is there upper bound on number of paths between a source and a destination?
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### If 8 (indistinguishable) blackboards are to be divided among 4 schools, how many divisions are possible if each school must receive 2 blackboards?

I attempted to come up with a solution. Please verify that it is correct or explain if there is anything wrong with it. Solution: Since each school must receive exactly 2 blackboards, we draw the ...
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### Divide 10 kids into 2 teams of 5 [on hold]

Given 10 kids divide into team A and team B of 5 kids each. Ans. (10!)/(5!5!) Given 10 kids divide into teams of 5 each. Ans. (10!)/(5!5!2!) Why? What's the difference
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### Prove $\binom{2n}{n}\geq\frac{4^n}{2n}$ [duplicate]

I want to prove that$$\binom{2n}{n} \geq \frac{4^n }{ 2n}$$ I tried to solve with Stirling formula and got to $$\binom{2n}{n} \geq C*\frac{4^n}{ 2n}.$$ I'm not sure how to continue since $C$ could ...
107 views

### Throw 40 dice and arrange them in a row - check my proof

Assume you throw $40$ dice and arrange them in a row so that you got a $40$-tuple. Then you throw antoher die. The result of this die indicates the number of the starting die of the $40$-tuple. E.g. ...
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### A question about weights [on hold]

I have a question, but I'm not sure if this question is for this group or another ( I seem to remember there's another group for this kind of questions though ): A guy has $100$ stones, and they're ...
Suppose there are $S$ slots in a cluster and $N$ individuals would pick $K$ slots each randomly from $S$. What's the expectation of the number of conflicts (each slot can only be picked by at most 1 ...