Discrete Mathematics and Its Applications with MathZone

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Homework 7: Due *Tuesday*, November 27, at *noon*. [Note that you have one day extension, but the quiz will be on Wednesday as usual.] Section 5.3: 2, 6 [by way of exception, here we want *numerical* values], 8, 12, 16, 18, 22, 40 Section 5.4: 4, 6, 8, 14 [prove only the first part, i.e. that C(n,i) < C(n,i+1) for i < floor(n/2)], 16, 22, 28 As in homework 6, in exercises in section 5.3 and in the first 3 exercises in section 5.4, you don't have to give numerical answers unless you are explicitely asked for them. For example, to question 2 in section 5.3, you should give your answer as 7! or as P(7), or as 1*2*3*...*7, but *not* as 5040. (Again, we'll give you no credit if you only provide a numerical answer, even if the answer is correct!!!) In some answers the formula might be more complicated, e.g. your answer to some question might be given by some formula whose components are combinations and/or permutations, e.g. "C(10,3) + C
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Unformatted text preview: (10,5)". There is many ways the same answer might be given. In this example the same answer can be given as P(10,3)/P(3) + P(10,5)/P(5), or as 10!/(7!*3!) + 10!/(5!*5!). But we don't want you to simplify these and re-write them as: 8*9*10/2*3 + 6*7*8*9*10/1*2*3*4*5, or even worse, cancelling these out and giving us an answer as 4*3*10 + 7*2*9*2 etc. All these formulas are express the same thing so numerically they are equivalent, but as in the previous homework the are two points: First, from an answer of the last type it's very hard for the grader to tell what's the logic that led you to giving this answer. Second, there's no point you should waste time computing these expressions numerically because this is not the point of these exercises. . ..ocuments/Dolores/UC%20Irvine-Harvest/ICS%206D/hmw7.htm [1/30/2008 12:06:49 PM]...
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