HW5Challenge - N nodes, and arbitrarily many cables? 2. (4...

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Math 100 Homework 5: Challenge Version! Martin H. Weissman 1. (4 points) In a network, there are N labelled “nodes” (sometimes called vertices). There are cables connecting some nodes to other nodes. There can be at most one cable connecting any pair of nodes. Nodes cannot be connected by cables to themselves. Therefore, every node can be attached to 0, 1, . .., or N - 1 other nodes. How many networks are there, composed of
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Unformatted text preview: N nodes, and arbitrarily many cables? 2. (4 points) Suppose that p is a prime number. Let S be a set with p elements. Let k be a natural number between 1 and p , exclusive . Prove that Sub ( S,k ) (the number of subsets of S with k elements) is divisible by p . You may use the existence and uniqueness of numbers into primes....
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This homework help was uploaded on 04/17/2008 for the course MATH 100 taught by Professor Weissman during the Fall '08 term at UCSC.

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