Transcription of MATH208: DISCRETE MATHEMATICS
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MATH208: DISCRETE MATHEMATICS
U N D M AT H E M AT I C SM AT H 2 0 8 :D I S C R E T EM AT H E M AT I C SD E PA R T M E N T O F M AT H E M AT I C ST H E U N I V E R S I T Y O F N O R T H DA KOTAC opyright 2017 UND Mathematicspublished by department of mathematicsthe university of north 2005,2006,2007,2008,2009,2014,2015,2016, 2017 University of North Dakota MathematicsDepartmentPermission is granted to copy, distribute and/or modify this document under the terms of the GNU FreeDocumentation License, any later version published by the Free Software Foundation; withno Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included inthe section entitled "GNU Free Documentation License".
30 The Binomial Theorem and Pascal’s Triangle 235 30.1 Combinatorial proof 235 30.1.1 Constructing combinatorial proofs 236 30.2 Pascal’s Triangle 238 30.3 The Binomial Theorem 239 30.4 Exercises 241. 13 31 Inclusion-Exclusion Counting 243 31.1 Inclusion-Exclusion principle 243
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