3! \times 3! \times 4! \times 2! \times 2! = 6 \times 6 \times 24 \times 2 \times 2
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- The 4 discoveries in the 18th century block can be arranged in \(4! = 24\) ways.
- The 2 discoveries in the 19th century block can be arranged in \(2! = 2\) ways.
- Therefore, the total number of distinct arrangements is the product of the arrangements of the blocks and the arrangements within each block:
- Calculate step-by-step:
- \times 24 = 864
- \times 2 = 1728
