I am trying to find the number of distinct coloring in the following problem:
Consider a 1*3 grid (shown as below) using 10 sticks and 8 balls. Color sticks with $m$ colors. How many ways are there to color the sticks with $m$ colors?
I try to use Burnside's lemma to count the distinct coloring, but I cannot find all the symmetric groups. Any help would be appreciated.