Let's say we have 3 numbers [1, 2, 3]. There are many ways to arrange these numbers but what I'm interested in is how many combinations can be made with these three numbers. This isn't too difficult to figure out, as raising the number of elements to the power of numbers in the combination can tell us this, example ;
[1, 2, 3] = 3 (number of elements) | [ _ _ _ ] = 3 (combination length)
so 3^3 would answer this question. 3^3 = 27. But I really want to know the amount of unique combinations possible if we allow the numbers to repeat, meaning ; [1, 1, 1] and [1, 1, 2] would each be unique combinations, but ; [1, 2, 1] and [2, 1, 1] would not count as they contain the same numbers as [1, 1, 2].
what equation can I apply to find the amount of unique number combinations with 'N' elements and 'K' combination length. Sorry for my terminology, poor explanation and possibly misleading title, I'm really not into mathematics but this question randomly came to me.