请教精英考试排列组合题解答思路

roseF

请教各位下面题的解题思路

we had to design a colour code for all the books in our class library. we decided to have 5 stripes on each book, we could colour each stripe in one of the three colours. it didn't matter if more than one stripe have the same colour, not even if they were adjacent.  but we could not have all the stripes the same colour.  how many different books could we code in this way?
like this

多谢啦

Junko

the answer is  160 !

Junko

160

jennyxio

teiyuau 发表于 2013-1-26 18:58
160

why?

roseF

the correct answer is 240. but i don't know how it is worked out.

roseF

这是精英考试题，选自Mathematics 100 mini Exams,  marked as "容易" ..
请高人指点

天眼

这是一道运用“乘法法则”的题目。
如果随便怎么涂色的话，有 3 x 3 x 3 x 3 x 3 = 243 种涂色方法。
但是，其中全部5个stripe全部颜色一样的有3种。
所以，243 - 3 = 240 种。

jasyangau

天眼 发表于 2013-1-26 20:52
这是一道运用“乘法法则”的题目。
如果随便怎么涂色的话，有 3 x 3 x 3 x 3 x 3 = 243 种涂色方法。
但是 ...

我也算的是240

kukupants

3^5-3=240