Problem 398

Cutting rope

Inside a rope of length `n`, `n`-1 points are placed with distance 1 from each other and from the endpoints. Among these points, we choose `m`-1 points at random and cut the rope at these points to create `m` segments.

Let E(`n`, `m`) be the expected length of the
second-shortest segment.
For example, E(3, 2) = 2 and E(8, 3) = 16/7.
Note that if multiple segments have the same shortest length the length
of the second-shortest segment is defined as the same as the shortest
length.

Find E(10^{7}, 100).
Give your answer rounded to 5 decimal places behind the decimal point.

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These problems are part of
Project Euler
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CC BY-NC-SA 2.0 UK
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