版权说明:本文档由用户提供并上传,收益归属内容提供方,若内容存在侵权,请进行举报或认领
文档简介
1、Chap 2 Combinatorial MethodsGhahramani 3rd edition1 Outline2.1 Introduction2.2 Counting principle2.3 Permutations2.4 Combinations2.5 Stirlings formula 2.1 IntroductionIf the sample space is finite and furthermore sample points are all equally likely, then P(A)=N(A)/N(S) So we study combinatorial ana
2、lysis here, which deals with methods of counting. 2.2 Counting principleEx 2.1 How many outcomes are there if we throw 5 dice?Ex 2.2 In tossing 4 fair dice, P(at least one 3 among these 4 dice)=?Ex 2.3 Virginia wants to give her son, Brian, 14 different baseball cards within a 7-day period. If Virgi
3、nia gives Brian cards no more than once a day, in how many way can this be done?Ex 2.6 (Standard Birthday Problem) P(at least two among n people have the same Bday)=?Counting principleThm 2.3 A set with n elements has 2n subsets.Ex 2.9 Mark has $4. He decides to bet $1 on the flip of a fair coin 4 t
4、imes. What is the probability that (a) he breaks even; (b) he wins money?(use tree diagram) 2.3 PermutationsEx 2.10 3 people, Brown, Smith, and Jones, must be scheduled for job interviews. In how many different orders can this be done?Ex 2.11 2 anthropology, 4 computer science, 3 statistics, 3 biolo
5、gy, and 5 music books are put on a bookshelf with a random arrangement. What is the probability that the books of the same subject are together?PermutationsEx 2.12 If 5 boys and 5 girls sit in a row in a random order, P(no two children of the same sex sit together)=?Thm 2.4 The number of distinguish
6、able permutations of n objects of k different types, where n1 are alike, n2 are alike, , nk are alike and n=n1+n2+nk isPermutationsEx 2.13 How many different 10-letter codes can be made using 3 as, 4 bs, and 3 cs?Ex 2.14 In how many ways can we paint 11 offices so that 4 of them will be painted gree
7、n, 3 yellow, 2 white, and the remaining 2 pink?Ex 2.15 A fair coin is flipped 10 times. P(exactly 3 heads)=?2.4 CombinationsEx 2.16 In how many ways can 2 math and 3 biology books be selected from 8 math and 6 biology books?Ex 2.17 45 instructors were selected randomly to ask whether they are happy
8、with their teaching loads. The response of 32 were negative. If Drs. Smith, Brown, and Jones were among those questioned. P(all 3 gave negative responses)=?CombinationsEx 2.18 In a small town, 11 of the 25 schoolteachers are against abortion, 8 are for abortion, and the rest are indifferent. A rando
9、m sample of 5 schoolteachers is selected for an interview. (a)P(all 5 are for abortion)=? (b)P(all 5 have the same opinion)=?Ex 2.19 In Marylands lottery, player pick 6 integers between 1 and 49, order of selection being irrelevant. P(grand prize)=? P(2nd prize)=? P(3rd prize)=?CombinationsEx 2.20 7
10、 cards are drawn from 52 without replacement. P(at least one of the cards is a king)=?Ex 2.21 5 cards are drawn from 52. P(full house)=?Ex 2.24 A professor wrote n letters and sealed them in envelopes. P(at least one letter was addressed correctly)=? Hint: Let Ei be the event that ith letter is addr
11、essed correctly. Compute P(E1UUEn) by inclusion-exclusion principle.CombinationsThm 2.5 (Binomial expansion)Ex 2.25 What is the coefficient of x2y3 in the expansion of (2x+3y)5?Ex 2.26 Evaluate the sumCombinationsEx 2.27 Evaluate the sumEx 2.28 Prove thatCombinationsEx 2.29 Prove the inclusion-exclusion principle.Ex 2.30 Distribute n distinguishable balls into k distinguishable cells so that n1 balls are distributed into the firs
温馨提示
- 1. 本站所有资源如无特殊说明,都需要本地电脑安装OFFICE2007和PDF阅读器。图纸软件为CAD,CAXA,PROE,UG,SolidWorks等.压缩文件请下载最新的WinRAR软件解压。
- 2. 本站的文档不包含任何第三方提供的附件图纸等,如果需要附件,请联系上传者。文件的所有权益归上传用户所有。
- 3. 本站RAR压缩包中若带图纸,网页内容里面会有图纸预览,若没有图纸预览就没有图纸。
- 4. 未经权益所有人同意不得将文件中的内容挪作商业或盈利用途。
- 5. 人人文库网仅提供信息存储空间,仅对用户上传内容的表现方式做保护处理,对用户上传分享的文档内容本身不做任何修改或编辑,并不能对任何下载内容负责。
- 6. 下载文件中如有侵权或不适当内容,请与我们联系,我们立即纠正。
- 7. 本站不保证下载资源的准确性、安全性和完整性, 同时也不承担用户因使用这些下载资源对自己和他人造成任何形式的伤害或损失。
最新文档
- 2024至2030年中国同轴信号防雷器数据监测研究报告
- 小学二年级奥数100题及答案
- 养老护理员前景
- 河北省唐山市玉田县2024-2025学年高三上学期11月期中考试 历史 含答案
- 广告牌承租合同范例
- 山东宗教建筑建设合同
- 深圳仓储物流租赁合同模板
- 办公楼地砖铺设工程合同
- 人员临时合同范例
- 建筑供电简易工程施工合同
- 建筑公司合规性评价报告
- 促销策略课件
- 大数据和人工智能知识考试题库600题(含答案)
- 2023年上海机场集团有限公司校园招聘笔试题库及答案解析
- 勘察质量及安全保障措施
- 高保真音频功率放大器
- 架桥机安全教育培训试卷
- 临时工用工协议书简单版(7篇)
- 国家电网公司施工项目部标准化管理手册(2021年版)线路工程分册
- 马克·夏加尔课件
- 沧州市基层诊所基本公共卫生服务医疗机构卫生院社区卫生服务中心村卫生室地址信息
评论
0/150
提交评论