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1、分类计数原理与分步计数原理 习题课20130402Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.Evaluation only.Evaluation only. Created with
2、 Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose
3、.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspos
4、e Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.例2、为了确保电子信箱的安全，在注册 时，通常要设置电子信箱密码。在某网站设 置的信箱中， （1）密码为4位，每位均为0到9这10个数字 中的一个数字，这样的密码共有多少个？（2）密码为4位，每位均为0到9这10个数字 中的一个，或是从A到Z这26个英文字母中的1 个。这样的密码共有多少个？ （3）密码为4到6位，每位均为0到9这10个数 字中的一个。这样的密码共有多少个？Evaluation only.Evaluation only. Created with Aspose.Slides for .NE
5、T 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.例 3. 一种号码锁有4个拨号盘，每个拨号盘上有从0 到9共十个数字,这4个拨号盘可以组成多少个四位数 的号码(各位上的数字允许重复)？首位数字不为0的 号码数是多少？首位数字是0的号码数又是多少？分析: 按号码位数,从左到右依次设置第一位、第二位、第三 位,第四位、需分为
6、 四步完成;第一步, m1 = 10; 第二步, m2 = 10; 第三步, m2 = 10，第四步 ， m4 = 10.根据分步记数原理, 共可以设置N = 101010 10 = 104种 四位数的号码。答:首位数字不为0的号码数是N =91010 10 = 9103 种,首位数字是0的号码数是 N = 11010 10 = 103 种。由此可以看出, 首位数字不为0的号码数与首位数字是0的号码数之和等于号码总数。Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5
7、.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.
8、 Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd
9、.例5.在所有的两位数中,个位数字大于十位数字 的两位数共有多少个？分析1: 按个位数字是2,3,4,5,6,7,8,9分成8类,在每一 类中满足条件的两位数分别是1个,2个,3个,4个,5个,6个,7 个,8 个.则根据分类记数原理共有 1 +2 +3 +4 + 5 + 6 + 7 + 8 =36 (个).分析2: 按十位数字是1,2,3,4,5,6,7,8分成8类,在每一类中 满足条件的两位数分别是8个,7个,6个,5个,4个,3个,2个,1个.则根据分类记数原理共有 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 36 (个)Evaluation only.Evaluat
10、ion only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.例6（1）要从甲、乙、丙三名工人中 选出两名分别上日班和晚班，有多少种不 同的选法？（2）某艺术组有9人，每人至少会钢 琴和小号中的一种乐器，其中7人会钢琴， 3人会小号，从中选出会钢琴
11、和会小号的各 一人，有多少种不同的选法？（3)用红、黄、蓝不同颜色的旗各三 面，每次升一面、两面、三面在某一旗杆 上纵向排列，共可以组成多少种不同的信 号？Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose
12、Pty Ltd.例7、（1）8张卡片上写着0,1,2,7共 8个数字，取其中的三张卡片排放在一起，可 组成多少个不同的三位数？（2）4张卡片的正、反面分别写有0与1 、2与3、4与5、6与7，将其中的3张卡片排放 在一起，共有多少个不同的三位数？(3)自然数2520有多少个正约数？(4)书架上原来并排放着5本不同的书， 现要插入三本不同的书，那么不同的插法有 多少种？Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose
13、.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspos
14、e Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.Evaluation only.Evaluatio
15、n only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.归纳推理 分类讨论 数学 源于生活数学 用于生活小结分类计数原理与分步计数原理分类计数原理：针 对的是“分类”问题 ，其各种方法互相 独立，用其中任何 一种方法都可以做 完这件事。分步计数原
16、理：针对 的是“分步”问题，各 个步骤的方法相互依 存，只有各个步骤都 完成了才算做完这件 事。都是有关做一件事情的 不同方法的种数的问题 。Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides
