How to express "$k$ things are the same" and "$n-k$ differ from each other as well as the $k$" as number of permutations?
I start with the obvious, which is the $n-k$ things differing from each other, which gives $(n-k)!$ permutations on the set "$n-k$".
However, I'm unsure about what counting the permutations of $n-k$ different things on the $k$ similar things means algebraically.
I believe $k$ similar things means that there's only one permutation, since with all orders of the $k$ elements, the sequence is the same.
But how do the two sets interact with each other? So what's the total amount of permutations?