组合一答案

组合数学第五版答案简介《组合数学第五版答案》是对组合数学第五版的习题答案进行整理和解答的参考资料。

组合数学是一门研究集合之间的组合方式和规律的数学科学。

它广泛应用于计算机科学、统计学、运筹学等领域，在算法设计、图论分析等方面有着重要的应用价值。

本文档包含了《组合数学第五版》中各章节的习题答案，主要内容涵盖了排列组合、图论、生成函数、递推关系、容斥原理等多个重要主题。

通过对这些习题的解答，可以帮助读者更好地理解组合数学的基本概念、方法和应用。

目录•第一章：基本概念和方法•第二章：排列组合•第三章：图论•第四章：生成函数•第五章：递推关系•第六章：容斥原理第一章：基本概念和方法1.习题1：证明排列的总数为n! (阶乘)。

2.习题2：计算组合数C(n, m)的值。

3.习题3：探究组合数的性质并给出证明。

第二章：排列组合1.习题1：计算排列数P(n, m)的值。

2.习题2：解决带有限制条件的排列问题。

第三章：图论1.习题1：证明图论中的握手定理。

2.习题2：解决图的着色问题。

第四章：生成函数1.习题1：利用生成函数求解递推关系。

2.习题2：应用生成函数解决组合数学问题。

第五章：递推关系1.习题1：求解递推关系的通项公式。

2.习题2：应用递推关系解决实际问题。

第六章：容斥原理1.习题1：理解容斥原理的基本思想并给出证明。

2.习题2：应用容斥原理解决计数问题。

结论通过对《组合数学第五版答案》中的习题进行解答，读者可以更好地掌握组合数学的基本概念和方法。

组合数学在计算机科学、统计学、运筹学等领域具有广泛的应用，通过学习和理解组合数学，读者可以提高解决实际问题的能力，并为进一步深入研究相关领域打下坚实的基础。

注：本文档中的习题答案仅供参考，请读者在独立思考和解答问题时加以思考和验证，以深入理解组合数学的核心概念和方法。

《初中生世界》九年级下学期语文阅读组合训练(一)答案1、《雨中登泰山》作者写到天街上的“小店”典型特点是（）[单选题] *新颖别致险峻狭窄(正确答案)古朴别致贫穷简陋2、1《南州六月荔枝丹》是一篇介绍荔枝的科学小品，属说明文。

[判断题] *对错(正确答案)3、42. 下列词语中没有错别字的一项是（）[单选题] *A．决择堕落狡辩相辅相成B．萦绕强褓浩劫愧不敢当C．绚丽枷锁拙劣怒不可遏(正确答案)D．授予荧屏开辟振耳欲聋4、1“江州司马青衫湿”中的江州司马是指王安石。

[判断题] *对(正确答案)错5、下列不属于《红楼梦》异名的一项是( ) [单选题] *A.《石头记》B.《风月宝鉴》C.《太虚幻境》(正确答案)D.《金陵十二钗》6、下列选项中加着重号字读音不相同的一项是（）[单选题] *A、消灭逍遥销路烟硝火药B、水淀纱锭靛蓝皮开肉绽(正确答案)C、菱角丘陵凌晨绫罗绸缎D、飘飞漂泊剽悍虚无缥缈7、“秩序”的读音是“chìxù”。

[判断题] *对错(正确答案)8、1“社”是土地神，“稷”是谷神，古文化中常用社稷代指国家。

这样的代称很多，如“桑梓”指家乡，“庙堂”指朝廷，“汗青”指史册。

[判断题] *对(正确答案)9、叶子出水很高，像亭亭的舞女的裙。

修辞格是（）[单选题] *夸张夸张拟人比喻(正确答案)10、1《致橡树》的作者是舒婷，中国当代朦胧诗派的代表诗人之一。

[判断题] *对(正确答案)错11、1“青，取之于蓝，而青于蓝；冰，水为之，而寒于水”此句与原文一致。

[判断题] *对错(正确答案)12、1荀子是继孔孟之后最著名的道家学者，朴素的唯物主义思想家。

[判断题] *对错(正确答案)13、6. 下列加双引号字的注音全都正确的一项是（）[单选题] *A．寒“噤”（jīn）蛮“横”（hèng）布“衾”（qīn）挑拨离“间”（jiàn）B．“彷”徨（páng）“皱”褶（zhé）“庇”护（bì）“强”词夺理（qiǎng）C．“襁”褓（qiǎng）“拙”劣（zhuō）“蠕”动（rǔ）怒不可“遏”（è）D．“瞭”望（liào）颠“簸”（bǒ）俯“瞰”（kàn）“拾”级而上（shè）(正确答案)14、1莫言是中国首位获得诺贝尔奖的作家，他借助《卖白菜》中母亲的形象，表达了自己对做人行事的看法：再穷也不能失掉志气，再穷也不能丢掉真诚。

2023年电气试验备考押题2卷合壹（带答案）（图片大小可自由调整）全文为Word可编辑，若为PDF皆为盗版，请谨慎购买！第一卷一.全能考点(共100题)1.【判断题】绝缘电阻表的接线端子包括“A”端子、“B”端子及“N”端子。

参考答案：×2.【判断题】牌号为DB-10的变压器油可用于气温不低于-50C的地区作为户外断路器、油浸电容式套管和互感器用油。

参考答案：√3.【判断题】工频电压和谐振过电压的波形是周期性的,持续时间较长,其波形为正弦波,频率为工频或工频的倍数。

参考答案：√4.【单选题】绝缘电阻表的屏蔽端子为()。

A、B、.C、.LD、.G参考答案：A5.【单选题】工频耐压试验时,采用测量球隙的()可以直接测量高压交直流耐压时的试验电压峰值和冲击试验时的冲击电压峰值。

A、闪络电压B、电晕电压C、击穿电压参考答案：C6.【单选题】测量试品的绝缘电阻时,如空气湿度较大,应在出线瓷套上装设屏蔽环接到绝缘电阻表的()。

A、.“G”端子B、.“L”端子C、.“N”端子参考答案：A7.【单选题】两个电阻串联接入电路,当两个电阻阻值不相等时,则()。

A、.两电阻的电流相等B、.电阻大的电流小C、.电阻小的电流小参考答案：A8.【单选题】在电路中,负载消耗功率等于电源产生的功率与内阻损耗的功率()。

A、.之和B、.之差C、.之积参考答案：B9.【判断题】直流电阻测量的方法有直流压降法及平衡电桥法。

参考答案：√10.【判断题】光辐射引起的气体分子的电离称为光电离。

参考答案：√11.【单选题】气体热状态下引起的电离称为()。

A、.碰撞电离B、.热电离C、.光电离参考答案：B12.【单选题】光辐射引起的气体分子的电离称为()。

A、.光电离B、.碰撞电离C、.热电离参考答案：A13.【判断题】对于同一电容C如接在不同频率的交流电路中时,频率越高则容抗越大。

参考答案：×14.【单选题】以下开关设备的工作原理()为采用增大压力来提高击穿电压。

组合数学第1章答案１.１ 从{}5021，，，⋅⋅⋅中找两个数{}b a ,，使其满足（1） 5||=-b a ；（2）5||≤-b a解：（1）根据5||=-b a 可得 55-=-=-b a b a 或 则有种种4545 共有90种。

（2）根据5||≤-b a 得 )50,,2,1(,55{⋅⋅⋅∈+≤≤-b a b a b则：当5≤b 时，有 1=b ， 61≤≤a ， 则有 6种 2=b ， 71≤≤a ， 则有7种 3=b ， 81≤≤a ， 则有8种 4=b ， 91≤≤a ， 则有 9种 5=b ， 101≤≤a ， 则有10种 当455≤<b 时，有 6=b ， 111≤≤a ， 则有 11种 7=b ， 122≤≤a ， 则有 11种. . . . . . . . . 45=b ， 5040≤≤a ， 则有11种 当5045≤<b 时，有 46=b ， 5041≤≤a ， 则有 10种 47=b ， 5042≤≤a ， 则有 9种 48=b ， 5043≤≤a ， 则有 8种 49=b ， 5044≤≤a ， 则有 7种 50=b ， 5045≤≤a ， 则有 6种故：共 种520)678910(21140=+++++⨯1.2 （1）先把女生进行排列，方案为5！，然后把女生看成1个人和7个男生进行排列，总方案数为5！×8！（2）女生不相邻，则先把男生进行排列，方案为7！再把女生插入男生之间的8个空位种的任意5个，总方案数为7！×58P（3）应该是A 女生x 女生y 女生z B,或是B 女生x 女生y 女生z A 的形式，从5个女生中选出3人进行排列，方案为35P ，考虑A,B 可以换位，方案为2×35P ，然后把这个看成一个整体，和剩下的2个女生，5个男生，一共7个人进行排列，总方案数2×35P ×8！1.3 m 个男生,n 个女生,排成一行,其中m,n 都是正整数,若 （a ）男生不相邻（m ≤n+1）；（b ）n 个女生形成一个整体； （c ）男生A 和女生B 排在一起； 分别讨论有多少种方案。

1第一章 排列组合1、 在小于2000的数中，有多少个正整数含有数字2？解：千位数为1或0，百位数为2的正整数个数为：2*1*10*10；千位数为1或0，百位数不为2，十位数为2的正整数个数为：2*9*1*10； 千位数为1或0，百位数和十位数皆不为2，个位数为2的正整数个数为：2*9*9*1；故满足题意的整数个数为：2*1*10*10+2*9*1*10+2*9*9*1＝542。

2、 在所有7位01串中，同时含有“101”串和“11”串的有多少个？ 解：（1） 串中有6个1：1个0有5个位置可以插入：5种。

（2） 串中有5个1，除去0111110，个数为()62-1＝14。

（或：()()4142*2+＝14）（3）串中有4个1：分两种情况：①3个0单独插入，出去1010101，共()53-1种；②其中两个0一组，另外一个单独，则有()()2*)2,2(4152-P 种。

（4）串中有3个1：串只能为**1101**或**1011**，故共4*2种。

所以满足条件的串共48个。

3、一学生在搜索2004年1月份某领域的论文时，共找到中文的10篇，英文的12篇，德文的5篇，法文的6篇，且所有的都不相同。

如果他只需要2篇，但必须是不同语言的，那么他共有多少种选择？ 解：10*12+10*5+10*6+12*5+12*6+5*64、设由1，2，3，4，5，6组成的各位数字互异的4位偶数共有n 个，其和为m 。

求n 和m 。

解：由1，2，3，4，5，6组成的各位数字互异，且个位数字为2，4，6的偶数均有P(5,3)=60个，于是：n = 60*3 = 180。

以a 1,a 2,a 3,a 4分别表示这180个偶数的个位、十位、百位、千位数字之和，则m = a 1+10a 2+100a 3+1000a 4。

因为个位数字为2，4，6的偶数各有60个，故 a 1 = (2+4+6)*60=720。

因为千（百，十）位数字为1，3，5的偶数各有3*P(4,2) = 36个，为2，4，6的偶数各有2*P(4,2) = 24个，故a 2 = a 3 = a 4 = (1+3+5)*36 + (2+4+6)*24 = 612。

作业习题答案习题二2.1证明：在一个至少有2人的小组中.总存在两个人.他们在组内所认识的人数相同。

证明：假设没有人谁都不认识：那么每个人认识的人数都为[1,n-1].由鸽巢原理知.n个人认识的人数有n-1种.那么至少有2个人认识的人数相同。

假设有1人谁都不认识：那么其他n-1人认识的人数都为[1,n-2].由鸽巢原理知.n-1个人认识的人数有n-2种.那么至少有2个人认识的人数相同。

2.3证明：平面上任取5个坐标为整数的点.则其中至少有两个点.由它们所连线段的中点的坐标也是整数。

证明：方法一：有5个坐标.每个坐标只有4种可能的情况：（奇数.偶数）；（奇数.奇数）；（偶数.偶数）；（偶数.奇数）。

由鸽巢原理知.至少有2个坐标的情况相同。

又要想使中点的坐标也是整数.则其两点连线的坐标之和为偶数。

因为奇数+奇数 = 偶数；偶数+偶数=偶数。

因此只需找以上2个情况相同的点。

而已证明：存在至少2个坐标的情况相同。

证明成立。

方法二：对于平面上的任意整数坐标的点而言.其坐标值对2取模后的可能取值只有4种情况.即：(0,0) ,(0,1) ,(1,0), (1,1).根据鸽巢原理5个点中必有2个点的坐标对2取模后是相同类型的.那么这两点的连线中点也必为整数。

2.4一次选秀活动.每个人表演后可能得到的结果分别为“通过”、“淘汰”和“待定”.至少有多少人参加才能保证必有100个人得到相同的结果？证明：根据推论2.2.1.若将3*（100-1）+1=298个人得到3种结果.必有100人得到相同结果。

2.9将一个矩形分成(m+1)行112mm+⎛⎫+⎪⎝⎭列的网格每个格子涂1种颜色.有m种颜色可以选择.证明：无论怎么涂色.其中必有一个由格子构成的矩形的4个角上的格子被涂上同一种颜色。

证明：（1）对每一列而言.有（m+1）行.m种颜色.有鸽巢原理.则必有两个单元格颜色相同。

（2）每列中两个单元格的不同位置组合有12m+⎛⎫⎪⎝⎭种.这样一列中两个同色单元格的位置组合共有12mm+⎛⎫⎪⎝⎭种情况（3）现在有112m m +⎛⎫+⎪⎝⎭列.根据鸽巢原理.必有两列相同。

1.1 题（宗传玉）从{1，2，……50}中找两个数{a ，b}，使其满足 （1）|a-b|=5； （2）|a-b|≤5； 解：（1）：由|a-b|=5⇒a-b=5或者a-b=-5，由列举法得出，当a-b=5时，两数的序列为（6，1）（7，2）……（50，45），共有45对。

当a-b=-5时，两数的序列为（1，6），（2，7）……（45，50）也有45对。

所以这样的序列有90对。

（2）：由题意知，|a-b|≤5⇒|a-b|=1或|a-b|=2或|a-b|=3或|a-b|=4或|a-b|=5或|a-b|=0；由上题知当|a-b|=5时 有90对序列。

当|a-b|=1时，两数的序列有（1，2），（3，4），（2，1）（1，2）……（49，50），（50，49）这样的序列有49*2=98对。

当此类推当|a-b|=2，序列有48*2=96对，当|a-b|=3时，序列有47*2=94对，当|a-b|=4时，序列有46*2=92对，当|a-b|=0时有50对所以总的序列数=90+98+96+94+92+50=520 1.2题（王星） 解：（a ）可将5个女生看作一个单位，共八个单位进行全排列得到排列数为： 8！×5！，（b ）用x 表示男生，y 表示空缺，先将男生放置好，共有8个空缺， Y X Y X Y X Y X Y X Y X Y X Y 在其中任取5个得到女生两两不相邻的排列数： C （8，5）×7！×5！（c ）先取两个男生和3个女生做排列，情况如下：6. 若A ，B 之间存在0个男生， A ，B 之间共有3个人，所有的排列应为 P6=C(5,3)*3!*8!*21．若A ，B 之间存在1个男生， A ，B 之间共有4个人，所有的排列应为 P1= C(5,1)*C(5,3)*4!*7!*22．若A ，B 之间存在2个男生，A ，B 之间共有5个人，所有的排列应为 P2=C(5,2)*C(5,3)*5!*6!*23．2．若A ，B 之间存在3个男生，A ，B 之间共有6个人，所有的排列应为 P3=C(5,3)*C(5,3)*6!*5!*24．若A ，B 之间存在4个男生，A ，B 之间共有7个人，所有的排列应为 P4=C(5,4)*C(5,3)*7!*4!*25．若A ，B 之间存在5个男生，A ，B 之间共有8个人，所有的排列应为 P5=C(5,5)*C(5,3)*8!*3!*2 所以总的排列数为上述6种情况之和。

中考冲刺完形阅读组合训练Group 1一、完型填空阅读下面短文，掌握大意，从每小题所给的A、B、C、D四个选项中选出最佳选项。

No one is born a winner. People make themselves into winners by their own 11 .I learned this lesson from an experience many years ago. I took the head 12 job at aschool in Baxley, Georgia. It was a small schoolwith a weak football program.It was a tradition for the school’s old team to play against the 13 team at the end of spring practice. The old team had no coach, and they didn’t even practice to 14 the game. Being the coach of the new team, I was excited because I knew we were going to win, 15 to my disappointment we were beaten. I couldn’t believe I had got into such a situation. Thinking hard about it, I came to realize that my team 16 not be the number one team in Georgia, but they were depending on me. I had to change my 17 about their ability and potential *.I started doing anything I could to help them build a little pride. Most important, I began to treat them like winners. That summer, When the other teams enjoyed 18 holidays, we met every day and practised passing and kicking the football.Six months 19 suffering our defeat*on the spring practice field, we won our first game and our second, and continued to improve. Finally, we faced the number 20 team in the state. I felt that it would be a victory* for us 21 we lost the game. But that wasn’t what happened. My boys beat the best team in Georgia, giving me one of the greatest thrills*of my life!From the experience I learnt a lot about 22 the attitude of the leader can affect the members of a team. Instead of seeing my boys as losers, I pushed and encouraged them. I helped them to see themselves 23 , and they built themselves into 24 .Winners are made, not 25 .11.A. luck B. tests C. efforts D. nature12.A. cooking B. reporting C. coaching D. playing13.A. successful B. excellent C. strong D. new14. A. cheer for B. prepare for C. help with D. finish with15. A. and B. but C. yet D. or16. A. might B. must C should D. need17. A. choice B. decision C. attitude D. attention18. A. our B. his C. her D. their19. A. before B. after C. during D. from20. A.one B. two C. three D. four21. A. even if B. because of C. so that D. as if22. A. what B. how C. when D. where23. A. honestly B. difficultly C. calmly D. differently24. A. leaders B. partners C. winners D. learners25. A. creative B. natural C. willing D. born一、阅读理解Passage 1While many young people were enjoying the summer vacation, Zach Bonner was working his hardest. Zach started walking from Valrico, Florida, his hometown, on Christmas, 2009. He reached Los Angeles nine months later in September, 2010. He covered a total of 2，478 miles and raised $120，000 for kids in need. Along the way, Zach attended school online. His mother, brother and sister took turns to walk or drive together with him.Although he is very young, Zach has a long history of helping others. When a terrible storm hit town in 2004, Zach, when six, pulled a wagon(小推车)through his community and collected food for people in need.He has raised $400，000 for his Little Red Wagon Foundation since then. It gives money to projects which help homeless children. In 2007, Zach began walking to support a children's charity(慈善组织)in Tampa, Florida. He finished his journey 23 days later, 280 miles away in Tallahassee. Then in the summer of 2009, he trekked about 670 miles from Atlanta to Washington, D．C., in just two months.“As long as there are homeless kids, I will never stop walking for them.” Zach says.( )1. What did Zach do during the summer vacation in 2010?A. He stayed at home to look after his family.B. He travelled to his hometown with his family.C. He joined in a school activity with other kids.D. He walked to collect money for kids in need.( )2. We can learn from Paragraph 2 that Zach________．A. began to help people at a very early ageB. made money to pay for his educationC. enjoyed playing around in his communityD. worked very hard for his family( )3. At what age did Zach start walking to support a Tampa children's charity?A. At six.B. At nine.C. At eleven.D. At twelve.( )4. The underlined word “trekked” in Paragraph 3 probably means “________”．A. 延伸B. 挖掘C. 跋涉D. 飞行( )5. Which of the following best describes Zach?A. Friendly and shy.B. Silly but lovely.C. Kind and helpful.D. Clever but lazy.Passage 2 From Nobody to SomebodyBrian was a funny student. He loved watching comedies(喜剧)best and hoped to become a comedy actor one day.When he heard about the talent show to be held at his school, Brian decided to take part in. He had never acted on stage(舞台)before, and he was very excited. But some students laughed at him. “You are not funny but silly，” Ken, one of his classmates, said to his face. “No one will like what you do，” another boy also said to him, loudly.Brian couldn't understand why they were so unkind to him. For a moment, he thought about giving up the show. But he remembered how much his friends liked his jokes, and also his teachers said he was very funny. So he decided to prepare for the show.Brian did a great job at the talent show. Everyone loved his performance, and he won the first prize! His teachers and friends were proud of him. Even so, Ken told Brian that he was not funny, and that he would never be successful. Brian didn't understand why Ken said so, but he realized that it had nothing to do with him. He confidently continued to work towards his goal.As the years went on, Brian met more people like Ken. “You'll do a terrible job，” they said to him. Luckily, most people encouraged him and some helped him to become even funnier. He got a lot of opportunities to perform in movies. He was even invited to appear on television. His fans thanked him because his comedies made them feel good when they were unhappy.Now Brian is a big comedy star! He is doing what he loves best. He never feels stressed like those unkind people, and he laughs all day long!( )1. What did Brian love best when he was a student?A. Going to school.B. Helping classmates.C. Watching comedies.D. Meeting new friends.( )2. Brian decided to prepare for the show because ________．A. his friends liked his jokesB. he was invited by a TV stationC. he wasn't busy acting in moviesD. Ken was expecting his performance( )3. After winning the first prize, Brian ________．A. began to understand KenB. became a teacher of actingC. encouraged others to join himD. continued to work towards his goal( )4. Brian's fans thanked him because his comedies brought them ________．A. successB. happinessC. luckD. pridePassage 3We have heard about people who have special memories. Recently there has been a report about a woman from Australia who can remember almost every detail(细节) of all the events in her daily life.Rebecca Sharrock, 25, is one of just 80 people worldwide who have been indentified(确定) as having Highly Superior Autobiographical Memory (HSAM，超级自传体记忆症). It means she can remember every small event—which most people would forget within(在……以内) days—as if it had happened just minutes ago.“I remember my mum putting me in the driver's seat of a car and taking a picture of me when I was 12days old，”she said. “That's my earliest memory. I remember every day since then. I can't tell all the dates exactly because I was too young to understand calendars, but I remember what I did that very day, what the weather was like and so on.”Rebecca can also re­experience taste. If she's eating something that she doesn't like, she thinks about Black Forest cake, her favorite food, and the memory will be so strong that she can nearly “taste” it.However, sometimes her memories prove(证明) to be painful. Because they're not just events that she remembers. “When I relive(再体验) memories, the feelings return, too，” Rebecca said.“For example, I remember falling over when I was three at my grandparents' house and hurting my left knee. Talking about it now, I feel painful in my left knee.”“At night, I have to sleep with the radio/recorder and a soft light on，”she added. “If it's too dark or quiet, my mind would be filled with all these memories and I can't sleep.”( )1. Which is NOT TRUE about Rebecca?A. She has special memories.B. She is from Australia.C. She is 25 years old.D. She can remember every detail of all the events.( )2. What happened to Rebecca on the day when she was 3 years old?A. She was identified as having HSAM.B. Her mother put her in a car and took a picture of her.C. She started to understand calendars.D. She hurt her left knee at her grandparents'.( )3. Whenever she is reliving her memories, ________．A. she is happyB. she experiences the feelings againC. she feels pain in her kneesD. she can taste her favorite food( )4. What is the result of having HSAM?A. She can remember every event in her daily life.B. She can re­experience taste.C. She can relive feelings.D. All the above.( )5. From the passage, we can infer(推断)that________．A. HSAM can do her good, but it also brings her painB. she feels painful if she recalls her experiencesC. she can fall asleep while she is re­experiencing memoriesD. HSAM can greatly improve her living conditionsPassage 4This year the US will honour(纪念) one of the country's most famous writers—Mark Twain(1835­1910). Most readers know that his real name was Samuel Longhorne Clemens, but how many know where the pen name “Mark Twain” came from?The answer shows Clemens' colourful early life before he became a writer. “Mark Twain” was the cry shouted on a ship when the ship entered a part of a river that was two fathoms(6 feet)deep. “Twain”is an old­fashioned way of saying “two”. Twain trained as a ship pilot on the Mississippi river for two years, a time that he wrote about in the humorous Life on the Mississippi(1883)．The famous river would become an important theme in many of his works—who could forget the journey of Huck and Jim along it in his most famous book, The Adventures of Huckleberry Finn(1884)?With little education, he had to teach himself how to write stories. Whenever possible, he would go to public libraries. There he spent much time reading and thinking, which greatly helped him with his writing.On the other hand, his life experiences gave him wonderful material to write about and attract readers. Twain wrote in a style that has been called “local colour” because it shows great knowledge of local people and their customs.This gift is very clear in the two books for which Twain is still celebrated today：The Adventures of Tom Sawyer(1876) and its follow­up The Adventures of Huckleberry Finn, which many people call “The Great American Novel”．The most amazing invention in the book is the voice of Huck himself. Huck did not enjoy schooling. It shows in the way he uses language, in a spoken style. Only a master like Twain could copy the way a young southern boy talked so well.( )1. What does the underlined word “gift” mean in the passage?A. Twain's talent for self­teaching.B. Twain's “local colour” writing style.C. Twain's good sense of humour.D. Twain's experiences as a ship pilot.( )2. According to the passage, what is the best part of The Adventures of Huckleberry Finn?A. The deep social meaning.B. The exciting life experiences.C. The special way that Huck talks.D. The nice view of the Mississippi.( )3. Which is the most suitable place in the passage for the sentence, “Twain did not come from the writer's background you might expect.”？A. At the beginning of Paragraph 2.B. At the beginning of Paragraph 3.C. At the beginning of Paragraph 4.D. At the beginning of Paragraph 5.( )4. What is the passage mainly about?A. Mark Twain's career as a great writer.B. Mark Twain's interest in describing local life.C. Mark Twain's achievements in American literature field.D. Mark Twain's life experiences which influenced his writing.Group 1参考答案完型填空：11-15 CCDBB 16-20 ACDBA 21-25 ABDCD阅读理解：Passage 1 DABCC Passage 2 CADB Passage 3 DDBDA Passage 4 BCCD。

第1章 排列与组合1.1 从{1,2,…,50}中找一双数{a,b}，使其满足：()5;() 5.a ab b a b -=-≤[解] (a) 5=-b a将上式分解，得到55a b a b -=+⎧⎨-=-⎩a =b –5，a=1，2，…，45时，b ＝6，7，…，50。

满足a=b-5的点共50-5=45个点. a = b+5，a=5，6，…，50时，b ＝0，1，2，…，45。

满足a=b+5的点共45个点. 所以，共计2×45=90个点. (b) 5≤-b a(610)511(454)1651141531+⨯+⨯-=⨯+⨯=个点。

1.2 5个女生，7个男生进行排列，(a) 若女生在一起有多少种不同的排列？ (b) 女生两两不相邻有多少种不同的排列？(c) 两男生A 和B 之间正好有3个女生的排列是多少？[解] (a) 女生在一起当作一个人，先排列，然后将女生重新排列。

（7＋1）!×5!=8!×5!＝40320×120=4838400(b) 先将男生排列有7!种方案，共有8个空隙，将5个女生插入，故需从8个空中选5个空隙，有58C 种选择。

将女生插入，有5!种方案。

故按乘法原理，有：7!×58C ×5!=33868800(种)方案。

(c) 先从5个女生中选3个女生放入A ，B 之间，有35C 种方案，在让3个女生排列，有3!种排列，将这5个人看作一个人，再与其余7个人一块排列，有(7+1)! = 8!由于A ，B 可交换，如图**A***B** 或 **B***A**故按乘法原理，有：2×35C ×3!×8!=4838400（种）1.3 m 个男生，n 个女生，排成一行，其中m ，n 都是正整数，若(a) 男生不相邻(m ≢n+1)； (b) n 个女生形成一个整体； (c) 男生A 和女生B 排在一起； 分别讨论有多少种方案.[解] (a) 先将n 个女生排列，有n!种方法，共有n+1个空隙，选出m 个空隙，共有mn C 1+种方法，再插入男生，有m!种方法，按乘法原理，有：n!×mn C 1+×m!＝n!×)!1(!)!1(m n m n -++×m!=)!1()!1(!m n n n -++种方案。