Problem 398Published on Sunday, 14th October 2012, 08:00 am; Solved by 227; 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(107, 100). Give your answer rounded to 5 decimal places behind the decimal point.