共可以组成多少个不同的七位数(其中“6”倒置可作“9”用,“9”倒置可作“6”用)?例2.连续射击n
gong ke yi zu cheng duo shao ge bu tong de qi wei shu ( qi zhong 6 dao zhi ke zuo 9 yong , 9 dao zhi ke zuo 6 yong )? li 2. lian xu she ji n
字可以是0，且其中数字可以重复)(2)一个小学生用十块分别写有0～9这十个数之一的硬纸片拼组数，问一
zi ke yi shi 0 qie qi zhong shu zi ke yi zhong fu )(2) yi ge xiao xue sheng yong shi kuai fen bie xie you 0 9 zhe shi ge shu zhi yi de ying zhi pian pin zu shu wen yi
)用0～9这十个数字组数，问一共可以组成多少个不同的含有七个数字的彩票号码?(提示:彩票号码中首位数
) yong 0 9 zhe shi ge shu zi zu shu wen yi gong ke yi zu cheng duo shao ge bu tong de han you qi ge shu zi de cai piao hao ma ?( ti shi : cai piao hao ma zhong shou wei shu
应适当补充有关“可重复”与“不允许重复”以及“步中有类”“类中有步”这些交叉型的问题。例如例1.(1
ying shi dang bu chong you guan ke zhong fu yu bu yun hu zhong fu yi ji bu zhong you lei lei zhong you bu zhe xie jiao cha xing de wen ti li ru li 1.(1
分类等问题，为正确应用两个基本原理打下坚实的基础。3.加强应用.除了认真完成课本上的例子和练习外，还
fen lei deng wen ti wei zheng que ying yong liang ge ji ben yuan li da xia jian shi de ji chu 3. jia qiang ying yong . chu le ren zhen wan cheng ke ben shang de li zi he lian xi wai hai
学生弄懂弄通什么叫做“完成了一件事”，什么叫“分步”，什么叫“分类”，什么情况下要分步，什么情况下要
xue sheng nong dong nong tong shen me jiao zuo wan cheng le yi jian shi shen me jiao fen bu shen me jiao fen lei shen me qing kuang xia yao fen bu shen me qing kuang xia yao
的辩证唯物主义观点。2.加强辩析.要用对比的手法分清两个基本原理的条件和结论，比较出它们的异同。要让
de bian zheng wei wu zhu yi guan dian 2. jia qiang bian xi . yao yong dui bi de shou fa fen qing liang ge ji ben yuan li de tiao jian he jie lun bi jiao chu ta men de yi tong yao rang
其次，要讲清“这两个原理的真确性由什么来保证”的问题，使学生形成或强化“数学来源明朗少女成功记于实践又服务于实践”
qi ci yao jiang qing zhe liang ge yuan li de zhen que xing you shen me lai bao zheng de wen ti shi xue sheng xing cheng huo qiang hua shu xue lai yuan ming lang shao nv cheng gong ji yu shi jian you fu wu yu shi jian
原理，然后再与课本相对照，进一步完善和精炼语句。由此调动学生的自主探索精神，培养学生的抽象概括能力。
yuan li ran hou zai yu ke ben xiang dui zhao jin yi bu wan shan he jing lian yu ju you ci diao dong xue sheng de zi zhu tan suo jing shen pei yang xue sheng de chou xiang gai kuo neng li
.加明朗少女成功记强引入.首先，应通过对一系列实际问题的分析讲解后，让学生们先用他们自己的语言归纳概括出这两个基本
. jia ming lang shao nv cheng gong ji qiang yin ru . shou xian ying tong guo dui yi xi lie shi ji wen ti de fen xi jiang jie hou rang xue sheng men xian yong ta men zi ji de yu yan gui na gai kuo chu zhe liang ge ji ben
果而减少了一点计算量而已。那么，如何切实做到加强两个基本原理的教学呢?我认为应从以下三个方面入手:1
guo er jian shao le yi dian ji suan liang er yi na me ru he qie shi zuo dao jia qiang liang ge ji ben yuan li de jiao xue ne ? wo ren wei ying cong yi xia san ge fang mian ru shou :1
列”、“组合”问题，利用其计算公式也只不过是减少了计算步骤和可以利用符号“pnm”或“cnm”表示结
lie zu he wen ti li yong qi ji suan gong shi ye zhi bu guo shi jian shao le ji suan bu zhou he ke yi li yong fu hao pnm huo cnm biao shi jie
关习题以及近几年来的高考题）并不单纯是教材中所定义的“排列”、“组合”问题。即明朗少女成功记便是教材中所定义的“排
guan xi ti yi ji jin ji nian lai de gao kao ti bing bu dan chun shi jiao cai zhong suo ding yi de pai lie zu he wen ti ji ming lang shao nv cheng gong ji bian shi jiao cai zhong suo ding yi de pai
问题与“组合”问题只不过是利用两个基本原理来解决的两个特殊的计数问题，而大量的问题（包括现实问题和有
wen ti yu zu he wen ti zhi bu guo shi li yong liang ge ji ben yuan li lai jie jue de liang ge te shu de ji shu wen ti er da liang de wen ti bao kuo xian shi wen ti he you
主要精力和大量时间花在“排列”与“明朗少女成功记组合”概念以及排列数与组合数公式的记忆与应用之上。孰不知，“排列”
zhu yao jing li he da liang shi jian hua zai pai lie yu ming lang shao nv cheng gong ji zu he gai nian yi ji pai lie shu yu zu he shu gong shi de ji yi yu ying yong zhi shang shu bu zhi pai lie
由于两个基本原理内容不多，“教参”中所分配的课时较少(约两课时)，因而容易将此关键内容一带而过，而把
you yu liang ge ji ben yuan li nei rong bu duo jiao can zhong suo fen pei de ke shi jiao shao ( yue liang ke shi ) yin er rong yi jiang ci guan jian nei rong yi dai er guo er ba
作用，而且作为一种解题方法，它还贯穿于整节内容的始终。因此，它理应成为我们重明朗少女成功记点把握的教学内容。然而，
zuo yong er qie zuo wei yi zhong jie ti fang fa ta hai guan chuan yu zheng jie nei rong de shi zhong yin ci ta li ying cheng wei wo men zhong ming lang shao nv cheng gong ji dian ba wo de jiao xue nei rong ran er
实加强两个基本原理的教学加法原理与乘法原理作为“排列与组合”单元中的基本原理，不仅起着理论上的奠基的
shi jia qiang liang ge ji ben yuan li de jiao xue jia fa yuan li yu cheng fa yuan li zuo wei pai lie yu zu he dan yuan zhong de ji ben yuan li bu jin qi zhe li lun shang de dian ji de
特，抽象概括程度高而结果又不易验算，因此一向认为这明朗少女成功记一单元是中学数学教学中较难教好学好的部分。一、要切
te chou xiang gai kuo cheng du gao er jie guo you bu yi yan suan yin ci yi xiang ren wei zhe ming lang shao nv cheng gong ji yi dan yuan shi zhong xue shu xue jiao xue zhong jiao nan jiao hao xue hao de bu fen yi yao qie
关于排列与组合教学的两点见解中学课本中关于排列与组合的内容虽然不多，但处理这类问题的思考和解答方式独
guan yu pai lie yu zu he jiao xue de liang dian jian jie zhong xue ke ben zhong guan yu pai lie yu zu he de nei rong sui ran bu duo dan chu li zhe lei wen ti de si kao he jie da fang shi du