Tagged Questions

Questions on discrete mathematics generally: "the study of mathematical structures that are fundamentally discrete rather than continuous"

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Please help me verify the following set equation from The Essence of Discrete Mathematics by Neville Dean

LaTeX markup suggested format: $\{y\in N_1 | y\le 4 \land (\exists x\in Z| x< 4 \land 6=yx\}$ Author's original post: {y:∈ N1 | y ≤ 4 Ʌ (∃x:∈Z | x < 4 . 6=y*x)} The first part of the equation ...
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Formula for sub and super sequence length given 2 strings

I have done a coding exercise where the problem was to compute the maximal length of a common substring given two strings. Consider strings as finite sequences with elements in the English alphabet ...
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Bijective proof? Examples?

I'm having trouble with understanding bijective proofs. I searched a lot, but I could not find a simple and well-explained resource. Can you give a simple example of a bijective proof with ...
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What is the expression for putting $n$ indistinguishable balls into $k$ indistinguishable cells?

I'm looking for the expressions for the number of ways in which $n$ indistinguishable balls can be placed into $k$ indistinguishable cells, with No cell being empty Some cells being empty I knew ...
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How to solve the following combinatorics problem?

There are $C$ kinds of colored balls, with $f_i$ being the frequency of each color $c_i$, such that $\Sigma_{i=1}^{C}f_i = n$, and $F= max(f_i)$. Let $G(x)$ be the number of ways in which these $n$ ...
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Coin Toss Probablities and Outcomes

I'm having a hard time with this question, but I did the best that I could. I would appreciate any help to correctly solve it. Suppose that a coin is tossed three times and the side that ...
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Five people are to be seated around a circular table. How many seatings are possible? (Full Q inside)

I'm attempting this question, but I'm a little unsure about my answers. The full question is: Five people are to be seated around a circular table. Two seatings are considered the same if one is a ...
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How many solutions are there to the equation $x + y + z + w = 17$?

How many solutions are there to the equation $x + y + z + w = 17$? I don't know if I'm doing this right, but I guessed that the solution would be $\binom{20}{3}$, which equals $1140$. Am I doing ...
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Question about the Pigeonhole Principle

The question is: Let $A = \{1,2,3,4,5,6,7,8\}$. If five integers are selected from $A$, must at least one pair of the integers have a sum of $9$? The book explains the solution by dividing the ...
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Probablity: 2 Urns

I'm trying to find the solution for this problem: There are 2 urns: urn 1 has 2 red balls and 1 blue ball and urn 2 has 1 red ball and 2 blue balls. You're supposed to randomly select one urn ...
So... last question that I have to do this semester... and of course it's one that I am completely wedged on. I am supposed to show that for any discrete subgroup $G$ of the isometry group in the ...