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Ben has 30 pencils in a box. Each of the pencils is one of 5 different colors, a
Ben has 30 pencils in a box. Each of the pencils is one of 5 different colors, a
游客
2024-01-12
29
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问题
Ben has 30 pencils in a box. Each of the pencils is one of 5 different colors, and there are 6 pencils of each color. If Ben selects pencils one at a time from the box without being able to see the pencils, what is the minimum number of pencils that he must select in order to ensure that he selects at least 2 pencils of each color?
选项
A、24
B、25
C、26
D、27
E、28
答案
C
解析
本(Ben)有5种不同颜色的铅笔,每种有6支,每次随意拿出1支,问最少拿出多少支,才能保证拿出每种颜色至少2支?
首先,有一种错误的理解方式是直接把每个颜色都拿出来2支,于是5×2=10支。但注意题目中问的是“保证每种颜色有2支”,如果只拿10支,并不知道能不能那么巧拿的就是5种颜色各2支。此时考生可以把自己想象成玩游戏时抽卡片的玩家,运气总是不好,每次想抽出来的东西总是抽不到。系统要求抽出每种颜色各2支就能成功,假如先抽出了2支蓝色,心想着蓝色够了可以不用再抽到蓝色了,但此时却接连把盒里的蓝色全抽出来了,继而又把盒里5种颜色里的4种都抽出来了,此时已经拿出了4×6=24支,而坏运气在这时已经走到了尽头,因为接下来不论拿哪2支,一定可以凑足5种颜色。所以一共是24+2=26支。答案为C选项。
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