Step 1: Concept:
The question requires ordering the standard biological taxonomic ranks (based on the Linnaean hierarchical system plus the modern Domain).
Step 2: Step-by-step Explanation:
• The standard taxonomic hierarchy from most specific (lowest rank, smallest group) to most broad (highest rank, largest group) is:
Species $\rightarrow$ Genus $\rightarrow$ Family $\rightarrow$ Order $\rightarrow$ Class $\rightarrow$ Phylum $\rightarrow$ Kingdom $\rightarrow$ Domain.
• The options use the "less than" ($<$) symbol. In the context of a hierarchy, this usually represents moving from the smallest, most exclusive structural subset up to the largest, most inclusive overarching category.
• Using the list provided, let's arrange them from smallest category to largest:
1. Family (B)
2. Orders (D)
3. Classes (E)
4. Phyla (C)
5. Domains (A)
• Therefore, the correct mathematical sequence using the $<$ operator is:
Family $<$ Orders $<$ Classes $<$ Phyla $<$ Domains.
• Substituting the letters: B $<$ D $<$ E $<$ C $<$ A.
Step 3: Final Answer:
The correct sequential arrangement is B $<$ D $<$ E $<$ C $<$ A, which matches option (C).