排列组合应用题一向被认为是中学数学教学中的难点,其主要原因是排列组合问题解题方法别具一格,不易掌握;计算结果繁杂,数值较大,不易验算,经常发生重复和遗漏现象而又不易查出。现将常见的错误解法以例题的形式写出,并指出出错的原因,以供读者参考。例1:第一组有三名男生二名女生,第二组有二名男生三名女生,第三组只有四名男生,从这三个小组每组选一人担任不同职务,且三人中只有一个女生,问共有多少种不同选法? 错解:第一类:第一组选派一个女生有C_2~1种,第二组选派一个男生有C_2~1种,第三组选派一名男生有C_4~1种。第二类:第一组派一名男生C_3~1,第二组 Arrangement and combination of applications has always been considered a difficulty in mathematics teaching in middle schools. The main reason is that the method for solving problems in permutation and combination problems is unique and difficult to grasp; the calculation results are complicated, the values ​​are large, and it is not easy to check the numbers. find out. The common error solutions are now written in the form of example questions and the reasons for the errors are provided for the reader’s reference. Example 1: There are three boys and two girls in the first group, two boys and three girls in the second group, and four boys in the third group. From each of the three groups, one person from each group is selected for a different position, and only one of the three girls How many kinds of different choices are there? Wrong solution: The first type: The first group chooses one female student to have C_2~1 species, the second group sends one male student to have C_2~1 species, and the third group chooses one male student to have C_4~ 1 species. The second category: The first group sent a male student C_3~1, the second group