I do not think your answer is correct. Look at simple case where n=3, k=2. Just enumerate all the possible cases, you will see it should be 6. But your answer is 3. And for n=4,k=2, the answer is 14, but yours is 24.
The answer should be nPk*k!*k^(n-k)/Q(n,k), where Q(n,k) is the recount...