In classical Chinese, 其 means 那个, 那, or 那些, and refers to people or things previously mentioned in the sentence. It stands to reason therefore, that 其中 (qízhōng）means "among the aforementioned" or 那里面, and denotes that something belongs to, is or is part of a bigger group. This is a little like "of which" in English, where you can say, "I have 3 ties, of which 2 are silk."
Category / Group / Context + 其中
In the last example sentence, 乐在其中 means "to find pleasure in" or maybe "there is joy involved with." This sounds awkward in English, but 其中 is often used in this abstract way.