试题与答案

设编号为1，2，3，4，5，6的六个茶杯与编号为1，2，3，4，5，6的六个茶杯

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题型：选择题

题目：

设编号为1，2，3，4，5，6的六个茶杯与编号为1，2，3，4，5，6的六个茶杯盖，将这六个杯盖盖在茶杯上，恰好有2 个杯盖与茶杯编号相同的盖法有

A．24种

B．135种

C．9种

D．360种

答案：

答案：B

题目分析：首先从6个号中选两个放到同号的盒子里，共有C62种结果，剩下的四个小球和四个盒子，要求球的号码与盒子的号码不同，首先第一个球有3种结果，与被放上球的盒子同号的球有三种方法，余下的只有一种方法，根据分步计数原理的结果解：由题意知本题是一个分步计数问题，首先从6个号中选两个放到同号的盒子里，共有C62=15种结果，剩下的四个小球和四个盒子，要求球的号码与盒子的号码不同，首先第一个球有3种结果，与被放上球的盒子同号的球有三种方法，余下的只有一种方法共有3×3=9种结果，根据分步计数原理得到共有15×9=135种结果．故选B．

点评：本题考查分步计数问题，本题解题的关键是选出球号和盒子号一致的以后4个小球和四个盒子的方法，本题是一个基础题

考点：排列与组合二项式定理与性质
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