Chapter 3.4（课件）- 《统计学基础（英文版）》同步教学（人民大学版）

Chapter Probability 3 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. 1 Larson/Farber 6th ed Chapter 1 Chapter Outline 3.1 Basic Concepts of Probability and Counting 3.2 Conditional Probability and the Multiplication Rule 3.3 The Addition Rule 3.4 Additional Topics in Probability and Counting 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. Section 3.4 Additional Topics in Probability and Counting . 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. Section 3.4 Objectives How to find the number of ways a group of objects can be arranged in order How to find the number of ways to choose several objects from a group without regard to order How to use the counting principles to find probabilities . 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. Permutations Permutation An ordered arrangement of objects The number of different permutations of n distinct objects is n! (n factorial) n! = n∙(n – 1)∙(n – 2)∙(n – 3)∙ ∙ ∙3∙2∙1 0! = 1 Examples: 6! = 6∙5∙4∙3∙2∙1 = 720 4! = 4∙3∙2∙1 = 24 . 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. Example: Finding the Number of Permutation of n Objects The objective of a 9 x 9 Sudoku number puzzle is to fill the grid so that each row, each column, and each 3 x 3 grid contain the digits 1 to 9. How many different ways can the first row of a blank 9 x 9 Sudoku grid be filled? Solution: The number of permutations is 9!= 9∙8∙7∙6∙5∙4∙3∙2∙1 = 362,880 ways . 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. Permutations Permutation of n objects taken r at a time The number of different permutations of n distinct objects taken r at a time ■ where r ≤ n . 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. Example: Finding nPr Find the number of ways of forming four-digit codes in which no digit is repeated. Solution: You need to select 4 digits from a group of 10 n = 10, r = 4 . 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. Example: Finding nPr Each year, 33 race cars start the Indianapolis 500. Ho