Cutting rope

Problem 398

Published on 14 October 2012 at 08:00 am [Server Time]

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(107, 100).
Give your answer rounded to 5 decimal places behind the decimal point.

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