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Unformatted text preview: Review Permutations and Combinations Some applications of counting techniques Fall 2010 EAS 305 Lecture Notes Prof. Jun Zhuang University at Buffalo, State University of New York September 10 ... 2010 Prof. Jun Zhuang Fall 2010 EAS 305 Lecture Notes Page 1 of 16 Review Permutations and Combinations Some applications of counting techniques Agenda for Today 1 Review Permutations and Combinations 2 Some applications of counting techniques Prof. Jun Zhuang Fall 2010 EAS 305 Lecture Notes Page 2 of 16 Review Permutations and Combinations Some applications of counting techniques Difference between permutations and combinations Combinations — not concerned w/order: ( a , b , c ) = ( b , a , c ). Permutations — concerned w/order: ( a , b , c ) 6 = ( b , a , c ). The number of permutations of n things taken ratatime is always as least as large as the number of combinations. In fact,. . . Prof. Jun Zhuang Fall 2010 EAS 305 Lecture Notes Page 3 of 16 Review Permutations and Combinations Some applications of counting techniques Remark Choosing a permutation is the same as first choosing a combination and then putting the elements in order, i.e., n ! ( n r )! = n r r ! So n r = n ! ( n r )! r ! . n r = n n r , n = n n = 1, n 1 = n n 1 = n . Prof. Jun Zhuang Fall 2010 EAS 305 Lecture Notes Page 4 of 16 Review Permutations and Combinations Some applications of counting techniques Examples for Combination Example: An NBA team has 12 players. How many ways can the coach choose the starting 5?...
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This note was uploaded on 10/31/2010 for the course EE 423 taught by Professor Mitin during the Spring '10 term at SUNY Buffalo.
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