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# prac02s - The University of Sydney School of Mathematics...

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The University of Sydney School of Mathematics and Statistics Solutions to Practice Class 2 MATH2069/2969: Discrete Mathematics and Graph Theory Semester 1, 2010 For some questions with a numerical answer, the answer is indicated in two forms, e.g. 12 2 = 6 . This is to give an indication of one way to obtain the answer; in a quiz, either form on its own would suﬃce, e.g. 12 2 alone or 6 alone. 1. Complete the Inclusion/Exclusion formulas: (a) | A B | = | A | + | B | − | A B | (b) | A B C | = | A | + | B | + | C | − | A B | − | A C | − | B C | + | A B C | 2. Complete the table giving the number of ways to make an unordered selection of k things from n possibilities: repetition allowed ( n + k - 1 k ) repetition not allowed ( n k ) Copyright c 2010 The University of Sydney 1

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3. Count the subsets of the set { A,B,C,D,E,F,G } : (a) which have 3 elements ( 7 3 ) = 35 (b) which have 3 elements and contain C ( 6 2 ) = 15 (c) whose intersection with { A,B,C,D } has size 2 ( 4 2 ) × 2 3 = 48 4. How many ways are there to select, from a barrel of 45 numbered balls: (a)
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prac02s - The University of Sydney School of Mathematics...

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