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Solution: We are assigning 12 distinct zones to 12 stages: 4 of one type (high-pressure), 3 of another (injectant), and 5 of a third (monitoring). Since the zones are distinguishable but stages of the same type are indistinct in labeling, the number of distinct arrangements is the multinomial coefficient:
Question: A pharmacologist is testing combinations of 3 neuroprotective drugs, 2 anti-inflammatory agents, and 1 cognitive enhancer from a pool of 6 neuroprotective, 5 anti-inflammatory, and 4 cognitive drugs. How many distinct treatment combinations can be formed if the order of selection does not matter?
Question: A geographer is analyzing satellite images of a coastal region divided into 15 zones, where sea level rise has affected exactly 6 of them. If the regions are indistinct except by location, how many ways can the affected zones be selected such that no two adjacent zones are both affected, assuming the zones are arranged in a straight line?

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