MIT6_042JS10_lec29_prob - Massachusetts Institute of...

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Unformatted text preview: Massachusetts Institute of Technology 6.042J/18.062J, Spring 10 : Mathematics for Computer Science April 16 Prof. Albert R. Meyer revised April 16, 2010, 1333 minutes In-Class Problems Week 10, Fri. Problem 1. A certain company wants to have security for their computer systems. So they have given every- one a name and password. A length 10 word containing each of the characters: a, d, e, f, i, l, o, p, r, s, is called a cword . A password will be a cword which does not contain any of the subwords fails, failed, or drop. For example, the following two words are passwords: adefiloprs, srpolifeda, but the following three cwords are not: a drop eis, failedrop s, drop e fails . (a) How many cwords contain the subword drop? (b) How many cwords contain both drop and fails? (c) Use the Inclusion-Exclusion Principle to find a simple formula for the number of passwords....
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This note was uploaded on 05/27/2011 for the course CS 6.042J taught by Professor Prof.albertr.meyer during the Spring '11 term at MIT.

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MIT6_042JS10_lec29_prob - Massachusetts Institute of...

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