MIT6_042JS10_lec31_prob

MIT6_042JS10_lec31_prob - Massachusetts Institute of...

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Massachusetts Institute of Technology 6.042J/18.062J, Spring ’10 : Mathematics for Computer Science April 23 Prof. Albert R. Meyer revised April 14, 2010, 1049 minutes In-Class Problems Week 11, Fri. Problem 1. We are interested in generating functions for the number of different ways to compose a bag of n donuts subject to various restrictions. For each of the restrictions in (a)-(e) below, find a closed form for the corresponding generating function. (a) All the donuts are chocolate and there are at least 3. (b) All the donuts are glazed and there are at most 2. (c) All the donuts are coconut and there are exactly 2 or there are none. (d) All the donuts are plain and their number is a multiple of 4. (e) The donuts must be chocolate, glazed, coconut, or plain and: • there must be at least 3 chocolate donuts, and • there must be at most 2 glazed, and • there must be exactly 0 or 2 coconut, and • there must be a multiple of 4 plain.
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