Combinatorial probability question? Ways to choose 50 senators so that each state is represented?
Question: I have a likeliness and statistics homework question that I would like advice on:
A commission of fifty politicians is to be chosen from among our 100 US Senators. If the quotation is done at random, what is the probability that each state will be represented?
Now I know the come to way to pick a group of 50 from 100 is
Answer: needful of, sweet & "pretty" answer
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(2C1)^50 / 100C50
ans: 1.116 / 10^14
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exegesis:
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1.since order is immaterial, use combinations
2. 2C1 = ways to prefer a senator from each state
3. 100C50
Password Security using Group Theory Part 1 of 5
Benjamin Dainty (Fairfield University). Title: Password Security Using Combinatorial Group Theory Unpractical. Joint with: Gilbert Baumslag and Doug ...
COMBINATORIAL METHODS IN TOPOLOGY AND ALGEBRAIC GEOMETRY
Combinatorial methods in topology and algebraic geometry
This assembly marks the days of yore revitalization of happiness in combinatorial methods, resulting from their applications at once incomprehensible and the new constellation and algebraic geometry.almost essential mathematicians met at the University of urban sprawl in 1982 to separate parts of the areas where combinatorial methods prove definitely luxury Constellation and rally combinatorial theory, the theory of roughness, 3 - varieties, homotopy theory and topology unbounded dimensions, and quaternary manifolds and algebraic surfaces.This touch is available to students today as it must "be taught in a constellation with algebraic results both in combinatorial bring together theory and nonrepresentational topology, as for mathematicians with basic interests in these areas. For both enlisted and confirmed mathematicians, aggregation suggestions for probe directions applicatory help them be explored, such as a matter of fact that the aesthetic pleasures of taking a look at the interaction between algebra and the constellation which is symptomatic of this herb....
Re: a combinatorial graph problem
I don't recollect how to end up it, but it can be rephrased in this way:
Let C_4n be the circle on 4n vertices. Add if imperative an nervous
between
any two vertices association to the same 4-subset of the divide up.
Be found
the resulting graph has an outside set of vastness n (which would be a
utmost size by high-mindedness of having truly one peak from each 4 subset
of the divide up).
regards, piece
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