What is the number of ways to color n objects with 3 colors if every color must be used at least once?
2009-11-13 9:35 am
What is the number of ways to color n objects with 3 colors if every color must be used at least once?
回答 (3)
2009-11-13 9:38 am
✔ 最佳答案
Simple.For the first object, we can use color 1
For the second object, we use color 2
For the third object, we use color 3.
After that, we can use any color we deem fit.
Apart from the 1st 3 objects, we have n ways of choosing the next color.
=> 1 * 1 * 1 * 3 * 3 * 3 ....
=> 1 * 3 ^ (n-3)
=> 3 ^(n-3)
2009-11-13 9:39 am
n x 3
= 3n
= 3n
2016-05-24 10:13 am
You can find an explanation of this problem online. It's solution number 1.8.29. I like to see things solved in a logical, deductive matter then just spewing formula. The deductive reasoning shown in the source follows the thought process required for mathematical proof which is more insightful.
收錄日期: 2021-04-25 13:06:53
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20091113013544AAuqyNr