Lecture 5 a notes

Lecture 5 a notes - Chapter 3 COMBINATORICS...

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Unformatted text preview: Chapter 3 COMBINATORICS (“COUNTING”) Reference: Devore 7th Ed., Section 2.3. Uses : Probability Gambling Magic (memory) tricks Optimal assignments, scheduling Statistical mechanics Quantum theory FUNDAMENTAL RULES OF COMBINATORICS 1. Fundamental Principle. If task A can be performed in M different ways and task B can be performed in N different ways then the sequence of tasks A and B can be performed in M × N different ways. 2. Definition of Factorials. For any positive integer n , n ! = n ( n- 1) ... (2)(1). Also we define 0! = 1. (Later we will learn how the gamma function is used to define factorials when n not necessarily an integer.) 3. Permutations. A permutation is an ordered sequence of objects. Given n distinct objects, the number of possible permutations (or ordered sequences) of those n objects is n !. 4. Permutations of Length n from N Objects. Given N distinct objects, the number of possible permutations of n of those objects is given by N ( N- 1) ... ( N- n + 1) = ( N !) / ( N- n )!....
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This note was uploaded on 02/13/2008 for the course ENGRD 2700 taught by Professor Staff during the Spring '05 term at Cornell.

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Lecture 5 a notes - Chapter 3 COMBINATORICS...

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