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Home » \Rightarrow x^2 + rac1x^2 = 7 - Coaching Toolbox

\Rightarrow x^2 + rac1x^2 = 7 - Coaching Toolbox

📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 5**Question:** A historian of science is examining sequences of scientific breakthroughs in different centuries. Suppose there are 3 major discoveries in the 17th century, 4 in the 18th century, and 2 in the 19th century. In how many distinct ways can these 9 discoveries be arranged in chronological order if discoveries from the same century must stay together?

📌 To solve this problem, we treat each century's group of discoveries as a single "block." Thus, we have three blocks:

📌 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)

📌 First, we calculate the number of ways to arrange the three blocks. Since there are 3 blocks, the number of arrangements is:

📌 Next, within each block, the discoveries can be arranged among themselves:

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