Ex07 - Review of Chapter 5 Review of Chapter 5 The Addition...

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Unformatted text preview: Review of Chapter 5 Review of Chapter 5 The Addition Principle The Addition Principle r 1 different objects in the first set, r 2 different objects in the second set, , r m different objects in the m th set, # of ways to select an object form one of the m sets: r 1 1 + r 2 2 ++ ++ r m . disjoint 2 AMS301, Summer 2009, Ning SUN The Multiplication Principle The Multiplication Principle A procedure -> m successive (ordered) stages: r 1 different outcomes in the first stage, r 2 different outcomes in the second stage, , r m different outcomes in the m th stage. # of different composite outcomes the total procedure: r 1 1 r 2 2 r m . Independent distinct 3 AMS301, Summer 2009, Ning SUN Summary Summary Arrangement (ordered outcome) or Distribution of distinct objects Selection (unordered outcome) or Distribution of identical objects No Repetition P ( n , r ) C ( n , r ) Unlimited Repetition n r C ( r + n-1, r ) Restricted Repetition P ( r; r 1 , r 2 , , r n )---- 4 AMS301, Summer 2009, Ning SUN Basic Formulas Basic Formulas ! ! ) , ( k n k n P = )! ( ! ! ) , ( k n k n k n k n C- = = ! !... ! ! ) ,..., , ; ( 2 1 2 1 n n r r r r r r r r P = 5 AMS301, Summer 2009, Ning SUN Integer Integer-solution solution-of of-an an-equation version equation version 1. The number of ways to select r objects with repetition from n different types of objects. 2. The number of ways to distribute r identical objects into n distinct boxes. 3. The number of nonnegative integer solutions to x 1 + x 2 ++ x n = r . 12 = 4 + 3 + 1 + 4 6 AMS301, Summer 2009, Ning SUN Probability Probability Probability = # desired outcomes # total outcomes 7 AMS301, Summer 2009, Ning SUN 5.2#16 5.2#16 What is the probability that a five-card poker hand has the following?...
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This note was uploaded on 02/13/2011 for the course AMS 301 taught by Professor Arkin during the Spring '08 term at SUNY Stony Brook.

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Ex07 - Review of Chapter 5 Review of Chapter 5 The Addition...

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