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Solution: Since the display is circular and two specific manuscripts must be adjacent, treat them as a single unit. In a circular arrangement, $ n $ distinct objects can be arranged in $ (n-1)! $ ways, so with 6 units (the pair + 5 other manuscripts), we have $ (6-1)! = 5! $ arrangements. However, the two manuscripts within the pair can be ordered in $ 2! $ ways. Thus, total arrangements are:
Question: A virologist is studying 10 viral strains, 4 of which are mutated. If she randomly selects 5 strains for analysis, what is the probability that exactly 2 of them are mutated?
Question: A historian discovers 9 letters from different scientists, including Einstein and Bohr, who insist on not being placed next to each other in a linear archive. How many valid arrangements are there?

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