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# HW8 - 3(3 points How many 6-letter words are there whose...

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EECS 203: DISCRETE MATHEMATICS Homework 8 Due Tuesday, November 20 at 4pm Put your name and discussion section number (not the meeting time) on the first page of your homework. Submit your homework to (a) CTools, as a PDF file, or (b) the drop box marked “EECS 203” in room EECS 2420. If neither (a) nor (b) is possible please turn in your homework at one of the discussion sections. 1. (4 points) A family has thirteen children: 5 identical quintuplets, two sets of 3 identical triplets, and 2 identical twins. How many distinguishable ways are there to seat the thirteen kids at a round table? (Identical siblings cannot be distinguished. If one seating pattern is a rotation of another then the two cannot be distinguished.) 2. (4 points) Five trick-or-treaters come to your door dressed up in different costumes. How many ways are there to distribute 10 chocolates and 14 lollipops to the trick-or-treaters if each must get at least one chocolate and one lollipop?
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Unformatted text preview: 3. (3 points) How many 6-letter words are there whose letters appear in alphabetical order? 4. The following questions refer to relations A ⊆ V × V , where V is a set with n elements. (a) (3 points) How many diﬀerent symmetric relations are there? (The answer should be a function of n .) (b) (3 points) How many anti-symmetric relations are there? (c) (3 points) How many relations are there that are both symmetric and anti-symmetric? (d) (3 points) Prove or disprove: if A 2 = A 4 then A = A 4 . (e) (3 points) Prove or disprove: if A is total then A 2 is total. (f) (3 points) If A is symmetric then which properties does A 2 have? (Reﬂexive, symmetric, anti-symmetric, total, transitive) 5. (3 points) S ⊆ Z × Z is the relation where for x, y ∈ Z , S ( x, y ) holds if and only if y = x +2 or y =-x . Give a simple description of S * and show how you derived your answer. 1...
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