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Unformatted text preview: EECS 203: DISCRETE MATHEMATICS Homework 8 Solutions 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.) There are ( 13 5 , 3 , 3 , 2 ) = 13! 5!3!3!2! ways to seat the children in a row and 13 different rotations of each seating pattern. (One reason all rotations are different is because the twins can never sit across from each other.) Therefore there are ( 1 13 ) 13! 5!3!3!2! distinguishable ways to seat the children at a round table. 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? First distribute chocolates one to each of the children. Do the same with the lollipops. There is exactly one way to do this. There now remain 5 chocolates and 9 lollipops. We now use the ”stars and bars” method for the rest. 5 indistinguishable chocolates can be distributed among 5 children in ( 9 4...
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- Fall '07
- Binary relation, Transitive relation, Symmetric relation, Total order, Antisymmetric relation, Symmetry in mathematics