# prac01s - The University of Sydney School of Mathematics...

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The University of Sydney School of Mathematics and Statistics Solutions to Practice Class 1 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 following principles: (a) (DiFerence Principle) If A is a subset of the ±nite set X ,then | X \ A | = | X |−| A | (b) (Pigeonhole Principle) If f : X Y is a function between nonempty ±nite sets, then there is some y Y such that | f - 1 ( y ) |≥ » | X | | Y | ¼ 2. Complete the table giving the number of ways to make an ordered selection of k things from n possibilities: repetition allowed n k repetition not allowed n ( k ) = n ( n 1) ··· ( n k +1) Copyright c ° 2010 The University of Sydney 1

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3. Suppose there are 135 students enrolled in a class. From that information alone,
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prac01s - The University of Sydney School of Mathematics...

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