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Each question on the survey offers 4 choices, and since there are 5 questions, and each is answered independently, we again apply the multiplication principle. The total number of ways to complete the survey is the product of the number of choices per question:
A student is designing a weekly study plan combining 3 subjects: Math, Science, and Language. Each week, the student chooses one subject per day (7 days), and each subject must be studied at least once during the week. How many distinct study plans satisfy this requirement?
We are to count the number of functions from a set of 7 days to 3 subjects (Math, Science, Language), such that each subject appears at least once. This is a classic inclusion-exclusion problem.

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