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排列组合的不少问题可构造盒中放球模型来求解。本文探讨两类盒中放球模型,并解答两题高考试题。模型一、将几个编号为①.②,③,…,(?)的小球放入有编号为1,2,3,…,n的几个盒子中,每盒放入一球,若球的编号与盒子的编号均不相同,则不同的放法有多少种? 设不同的放法有B种。首先考虑①球放入2盒内,可分为两类: (1)②球放入1盒,则转化为其余n-2个球放入,1-2个盒子的情况,显然有Bn-2种;
Many problems in permutation and combination can be solved by constructing a ball-in-box model. This article discusses two types of boxes in the ball model, and answer questions in two questions. Model 1. Put several balls numbered 1.2, 3, ..., (?) into several boxes numbered 1,2,3,...,n, and put a ball into each box. The number of the ball is not the same as the number of the box. How many different types of play are there? There are B types of different play methods. First consider that 1 ball is put into 2 boxes and it can be divided into two categories: (1) 2 balls put into 1 box, then into the remaining n-2 balls to put in, 1-2 boxes in the case, apparently Bn- 2 kinds;