lec09-鸽洞原理和排列组合
21页1、Lecture 9: Counting Principles,Discrete Mathematical Structures: Theory and Applications,Discrete Mathematical Structures: Theory and Applications,2,Learning Objectives,Learn the basic counting principlesmultiplication and addition Explore the pigeonhole principle Learn about permutations Learn about combinations,Discrete Mathematical Structures: Theory and Applications,3,Learning Objectives,Learn about binomial coefficients and explore the algorithm to compute them Discover the algorithms to ge
2、nerate permutations and combinations Become familiar with discrete probability,Discrete Mathematical Structures: Theory and Applications,4,Basic Counting Principles,Discrete Mathematical Structures: Theory and Applications,5,Basic Counting Principles,Discrete Mathematical Structures: Theory and Applications,6,Basic Counting Principles,There are three boxes containing books. The first box contains 15 mathematics books by different authors, the second box contains 12 chemistry books by different a
3、uthors, and the third box contains 10 computer science books by different authors. A student wants to take a book from one of the three boxes. In how many ways can the student do this?,Discrete Mathematical Structures: Theory and Applications,7,Basic Counting Principles,Suppose tasks T1, T2, and T3 are as follows: T1 : Choose a mathematics book. T2 : Choose a chemistry book. T3 : Choose a computer science book. Then tasks T1, T2, and T3 can be done in 15, 12, and 10 ways, respectively. All of th
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