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MIT6_042JS10_lec26_prob

# MIT6_042JS10_lec26_prob - Massachusetts Institute of...

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Massachusetts Institute of Technology 6.042J/18.062J, Spring ’10 : Mathematics for Computer Science April 9 Prof. Albert R. Meyer revised April 10, 2010, 732 minutes In-Class Problems Week 9, Fri. Problem 1. A license plate consists of either: • 3 letters followed by 3 digits (standard plate) • 5 letters (vanity plate) • 2 characters – letters or numbers (big shot plate) Let L be the set of all possible license plates. (a) Express L in terms of A = { A, B, C, . . . , Z } D = { 0 , 1 , 2 , . . . , 9 } using unions ( ) and set products ( × ). (b) Compute | L | , the number of different license plates, using the sum and product rules. Problem 2. An n -vertex numbered tree is a tree whose vertex set is { 1 , 2 , . . . , n } for some n > 2 . We define the code of the numbered tree to be a sequence of n 2 integers from 1 to n obtained by the following recursive process: If there are more than two vertices left, write down the father of the largest leaf a , delete this leaf , and continue this process on the resulting smaller tree.

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