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📰 Question: A science educator is developing a 6-day interactive virtual lab path, where each dayâs activity involves one of 4 experiment types: Physics, Chemistry, Biology, or Astronomy. If each experiment type must be used at least once during the week and activities are distinguishable only by type, how many distinct 6-day sequences can be designed?
📰 Solution: We are counting the number of 6-day sequences using 4 experiment types (P, C, B, A), where each type appears at least once, and sequences are ordered. This is a classic inclusion-exclusion problem: counting the number of surjective functions from a 6-day sequence to 4 experiment types.
📰 Total sequences without restriction: $ 4^6 $
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