The following table provides a comparison of the number of faculty members in each department at a particular college to the student head count in that department and the number of class sections in that department in the Spring semester. Use this information to answer the questions.

1. Determine the ratios for each department: \(S\) to \(C, C\) to \(T, S\) to \(T, F\) to \(P\)
2. What are the units of the ratios that you found?
3. Which of these pairs, if any, has a constant part to part ratio? State the ratio.
4. Does it appear that the total number of faculty positions were allocated to each department based on student head count, the number of class sections, or neither? Justify your answer.

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Department Mathematics English History Science (S) Student Head Count 4800 2376 1536 2880 (C) Class Sections 120 108 48 96 (T) Total Faculty 30 27 12 24 24 (F) Full-Time Faculty 10 6 4 00 8 (P) Part-Time Faculty 20 20 18 00 8 16