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下面是一道排列组合的常规题.题目6本不同的书,按下列要求各有多少种不同的选法:分给甲、乙、丙三人,每人至少1本.分析可以分为三类情况:1“2、2、2型”的分配情况,有C_6~2C_4~2C_2~2=90种方法;2“1、2、3型”的分配情况,有C_6~1C_5~2C_3~3A_3~3=360种方法;3“1、1、4型”的分配情况,有C_6~4A_3~3=90种方法,所以,一共有90+360+90=540种方法.完成此题后,我们会自然地思考一般情形的解决方法.于是提出以下问题:
The following is a list of regular questions arranged in combination. Title 6 different books, according to the following requirements each have a number of different options: A, B, C three, each at least 1. Analysis can be divided into three categories Situation: There are C_6 ~ 2C_4 ~ 2C_2 ~ 2 = 90 kinds of methods for the distribution of “2,2,2 type”, and the distribution of “1,2,3 type” is C_6 ~ 1C_5 ~ There are 90 methods of C_6 ~ 4A_3 ~ 3 = 90, so there are totally 90 + 360 + 90 = 540 methods. After completing this question, we will naturally think about the solution to the general situation and then ask the following questions: