Consider the following two statements about regular languages: $S_1$: Every infinite regular language contains an undecidable language as a subset. $S_2$: Every finite language is regular. Which one of the following choices is correct?

Let us evaluate both statements:

1. Statement $S_1$: An infinite regular language $L$ is a countably infinite set of strings. The power set of $L$, $\mathcal{P}(L)$, is uncountably infinite with cardinality $2^{\aleph_0}$. However, the set of all decidable (Turing-decidable) languages is countably infinite (cardinality $\aleph_0$) because every decidable language is decided by some standard Turing machine, and the set of Turing machines is countable. Therefore, uncountably many subsets of $L$ are undecidable. Hence, every infinite regular language contains an undecidable language as a subset. Thus, $S_1$ is true.

2. Statement $S_2$: Any finite language $L = \{w_1, w_2, \dots, w_k\}$ can be expressed by the regular expression $w_1 + w_2 + \dots + w_k$. Since a regular expression exists for any finite language, every finite language is regular. Thus, $S_2$ is true.

Both $S_1$ and $S_2$ are true, so the correct option is (C).