“至多”类型的组合题,利用补集的方法从整体中排除不满足条件的部分即可。还有一类“至少一个”的组合题,一些杂志都是通过分类或列表逐一讨论,这样解比较麻烦,下面介绍一种简单的方法——插入闸板法。例将组成篮球队的12个名额分给7个学校,每校至少有1个名额,问名额分配方法有多少种? 解 12个名额可以看作把排成一行的12个1分成7份的方法数,这样用6个闸板 The “total” type of combination question uses the complement method to exclude parts that do not satisfy the condition from the whole. There is also a category of “at least one” combination of questions, some magazines are discussed by category or list one by one, this solution is too much trouble, here’s a simple way - insert the gate method. For example, the 12 places that make up the basketball team will be distributed to 7 schools, each school will have at least 1 place, and how many kinds of place allocation methods will be asked? The solution of 12 places can be seen as dividing 12 1 in a row into 7 places. Number of methods, so with 6 rams