I recently learned about multisets and am told that a simultaneous throw of k-dice is a k-Multiset over the set of {1,2,3,4,5,6}.. mathematically expressed as $\frac{(n+1-k)!}{k!(n-1)!}$. However intuitively, I thought the number of outcomes would be $6^k$ and did a search and came across this other stackexchange question. Am unfortunately still rather confused. (Probability of predicting, then throwing, a particular multiset for 5 dice.)
Question is, what then is the correct method in determining the number of outcomes of a simultaneous cast of k dice?
As far as I understand, a multiset should be used when we're just interested in finding the number of RESULTS and $6^k$ when we're interested in the number of WAYS to throw every possible result? Am I on the right track?