Today I continued learning the ordered sets with replacement with more details,

Let's say we are going to pick 4 objects from 3 objects (labeled as A, B and C,with replacement).

First, AAAA, there are 3 ways to choose, one way of arrangement, so it is 

3 * 1 = 3

Second, AAAB, there are 6 ways to choose, 4 ways of arrangement,

6 * 4 =24

Third, AABB, there are 3 ways to choose, 6 ways of arrangement,

3 * 6 = 18

Fourth, AABC, there are 3 ways to choose, 12 ways of arrangements,

3 * 12 = 36

So totally it is 3 + 24 +18 + 36 = 81 equals 3 powers to the 4 = 3 * 3 * 3 *3 =81

awesome, you've learned it, keep going, Tiger : )