Prove that $L = \{0^n1^m \mid n ≥ 10, m ≤ 50\}$ is regular and that any subset of it is regular

Question

Question: Let L = {0ⁿ1^m, n ≥ 10 m ≤ 50}. Prove that this is a regular language and that any subset of it is also regular.

Answer or approach: 0 is regular, 1 is regular since any symbol in ∑ is regular. Then 1ⁿ, n≥10 is regular, because of concatenation of regular languages. Similar argument for 1^m. Then 1ⁿ1^m is regular because concatenation of regular languages is regular.

Not sure about the subset begin regular part...

Is my answer/approach a good place to start, or am I going the wrong way?

Should I design a NFA/DFA for it instead? I think doing so would be harder....

any hints or guidance would be greatly appreciated.

thanks