## Cutting rope

### Problem 398

Published on Sunday, 14th October 2012, 08:00 am; Solved by 229; Difficulty rating: 55%
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.