First, we calculate the number of ways to arrange the three blocks. Since there are 3 blocks, the number of arrangements is:
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- 1 block of discoveries from the 17th century (3 discoveries)
- 1 block of discoveries from the 18th century (4 discoveries)
- 1 block of discoveries from the 19th century (2 discoveries)
- Next, within each block, the discoveries can be arranged among themselves:
- The 3 discoveries in the 17th century block can be arranged in \(3! = 6\) ways.
- The 4 discoveries in the 18th century block can be arranged in \(4! = 24\) ways.
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