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Unformatted text preview: 235 Combinatorics 20 Generalized Pigeonhole Principle (1) •  Theorem: If N objects are placed into k boxes then there is at least one box containing at least •  Example: In any group of 367 or more people, at least two of them must have been born on the same date. CSCE 235 Combinatorics 21 Generalized Pigeonhole Principle (2) •  A probabilis5c generaliza5on states that –  if n objects are randomly put into m boxes –  with uniform probability –  (i.e., each object is place in a given box with probability 1/ m) –  then at least one box will hold more than one object with probability CSCE 235 Combinatorics 22 Generalized Pigeonhole Principle: Example •  Among 10 people, what is the probability that two or more will ha...
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