The key size of an ideal block cipher
Ideally, each key $k$ select a permutation of all possible permutations $2^n!$ for a block cipher with block size $n$. So when we say 128-bit key we expect that they represent $2^{128}$ permutations from possible ones. Some keys might be very bad, maybe just inverting the plaintext or some acts as a counter, we don't know.

Your calculations are correct if the random selection has no collisions, i.e. there may be two keys that represent the same permutations. We don't expect this collision since $2^{128}$ is very small compared to $2^n!$.

In general, we don't talk about the number of permutations that the key-size represents. We talk about the provided security by key length in bits.