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LEC_EAS305_F11_0909

# LEC_EAS305_F11_0909 - Review Permutations and Combinations...

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Review Permutations and Combinations Some applications of counting techniques Fall 2011 EAS 305 Lecture Notes Prof. Jun Zhuang University at Bu alo, State University of New York September 9 ... 2011 Prof. Jun Zhuang Fall 2011 EAS 305 Lecture Notes Page 1 of 16

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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 2011 EAS 305 Lecture Notes Page 2 of 16
Review Permutations and Combinations Some applications of counting techniques Di erence 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 r -at-a-time is always as least as large as the number of combinations. In fact,. . . Prof. Jun Zhuang Fall 2011 EAS 305 Lecture Notes Page 3 of 16

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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 0 = n n = 1, n 1 = n n - 1 = n . Prof. Jun Zhuang Fall 2011 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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