I asked a question at this Number of arrangements of red, blue, and green balls in which a maximum of three balls of the same color are placed in the five slots. Now the scenario is the same
I have a bag of three balls (look at the link)
and I have 5 slots.. Every time I pull a ball from the bag I placed it in a slot. I keep randomly pulling balls from the bag and fill five slots..when all five slots are filled, repeat the process
I still want to number of arrangements of red, blue, and green balls in which a maximum of three balls of the same color are placed in the five slots
I found an interesting article by Roberto Frucht (1966), Permutations with limited repetitions that derives a formula to do this.
I want to find the results using this breakthrough formula:
for "the number of $r$-permutations (called variations, r at a time in the older literature) with limited repetition, where each one of the $n$ different things to be permuted may appear at most $s$ times."
Note: In the professor's research he gives an example that shows how many permutations can be computed if 4 items are chosen from 7 items where only a maximum of two items and repeat itself in the arrangement. Note the formula shows that Bell polynomials and Stirling Strings of the second kind play a significant role in deriving the formula.
I am requesting some practical help as to how to use this formula.Specifically, plugging values in and getting the expected results.