What's time complexity of this algorithm for finding all combinations?

Question

Combinations
Given two integers n and k, return all possible combinations of k numbers out of 1 ... n.
For example

Answer 1

I don't think it is O(n^k). Because think about it. Let's assume n=100 and k=2. According to your complexity it will 100 to the power 2. But if it is n=100 and k=10, it will be 100 to the power of 10. But if you think about it, there are far more combinations with n=100,k=2 than n=100,k=10. The complexity is actually is the actual formula: which is n!/(k!(n-k)!). And the complexity therefore will be O(n!/k!(n-k)!).