Final answer:
There are 48 possible course selections for a freshman taking one course in each of five different areas, determined by multiplying the number of options in each course category together.
Step-by-step explanation:
To determine how many course selections are possible for a freshman who takes one course in each area during her first semester, we can use the fundamental counting principle. This principle states that if there are n ways of doing one thing, and m ways of doing another thing after that, then there are n x m ways of doing both things.
In this scenario, the number of ways to select one course from each area is simply the product of the number of options in each category. Since the college offers 2 history courses, 2 science courses, 1 mathematics course, 4 philosophy courses, and 3 English courses, the total number of course selections is:
2 (History) x 2 (Science) x 1 (Mathematics) x 4 (Philosophy) x 3 (English)
By multiplying these together, we get:
2 x 2 x 1 x 4 x 3 = 48 possible course selections.