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Unformatted text preview: Outline Counting Techniques Lecture 6 Chapter 2: Introduction to Probability Michael Akritas Michael Akritas Lecture 6 Chapter 2: Introduction to Probability Outline Counting Techniques Counting Techniques Why Count? The Product Rules Permutations Combinations Michael Akritas Lecture 6 Chapter 2: Introduction to Probability Outline Counting Techniques Why Count? The Product Rules Permutations Combinations Michael Akritas Lecture 6 Chapter 2: Introduction to Probability Outline Counting Techniques Why Count? The Product Rules Permutations Combinations First, in s.r. sampling from a population of N units every group of n has the same chance of being selected. Michael Akritas Lecture 6 Chapter 2: Introduction to Probability Outline Counting Techniques Why Count? The Product Rules Permutations Combinations First, in s.r. sampling from a population of N units every group of n has the same chance of being selected. Thus, for the probability of a particular sample being selected, we need to know Michael Akritas Lecture 6 Chapter 2: Introduction to Probability Outline Counting Techniques Why Count? The Product Rules Permutations Combinations First, in s.r. sampling from a population of N units every group of n has the same chance of being selected. Thus, for the probability of a particular sample being selected, we need to know I How many samples of size n can be formed from N units? Michael Akritas Lecture 6 Chapter 2: Introduction to Probability Outline Counting Techniques Why Count? The Product Rules Permutations Combinations First, in s.r. sampling from a population of N units every group of n has the same chance of being selected. Thus, for the probability of a particular sample being selected, we need to know I How many samples of size n can be formed from N units? The answer to this questions is the number of combinations of n objects selected from N , Michael Akritas Lecture 6 Chapter 2: Introduction to Probability Outline Counting Techniques Why Count? The Product Rules Permutations Combinations First, in s.r. sampling from a population of N units every group of n has the same chance of being selected. Thus, for the probability of a particular sample being selected, we need to know I How many samples of size n can be formed from N units? The answer to this questions is the number of combinations of n objects selected from N , denoted by ( N n ) , and equals N n = N ! n !( N n )! , where k ! = 1 2 k . Michael Akritas Lecture 6 Chapter 2: Introduction to Probability Outline Counting Techniques Why Count? The Product Rules Permutations Combinations First, in s.r. sampling from a population of N units every group of n has the same chance of being selected. Thus, for the probability of a particular sample being selected, we need to know I How many samples of size n can be formed from N units?...
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 Spring '00
 Akritas
 Counting, Probability

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